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UMDMATH 140GulickFall

MATH 140- Final Exam Guide - Comprehensive Notes for the exam ( 76 pages long!)

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Math 140 lecture 1 precalculus review and limits. Quadratic formula: ex: (cid:884)(cid:2871) (cid:885)(cid:2870) =(cid:882) (cid:1858) =(cid:882, = (ci
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UMDMATH 140GulickFall

MATH 140- Midterm Exam Guide - Comprehensive Notes for the exam ( 76 pages long!)

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Math 140 lecture 1 precalculus review and limits. Quadratic formula: ex: (cid:884)(cid:2871) (cid:885)(cid:2870) =(cid:882) (cid:1858) =(cid:882, = (ci
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UMDMATH 140AllFall

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UMDMATH 140AllSpring

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UMDMATH 140GulickFall

MATH 140 Study Guide - Final Guide: Cosc, Paq, Paper Cup

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UMDMATH 140GulickFall

MATH 140 Lecture Notes - Lecture 38: Ellipse, Hyperbola

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Math140 lecture 38 conic sections (cont. ) Let p 1 and p 2 be distinct points in the plane. Let | p 1 p 2 | > 2 a , where a is a positive. The points p
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UMDMATH 140GulickFall

MATH 140 Lecture Notes - Lecture 37: Ellipse

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Math140 lecture 37 conic sections (parabolas and ellipses) Let p be a point not on a given line l . P and l form a parabola: let p = (0, c , let the li
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UMDMATH 140GulickFall

MATH 140 Lecture 36: Exam 4 Review

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( 1 + 2 1 = 0 (2. Explain: since ln x is increasing on [1, 2], the left sum is automatically less than n x dx l. 2 w w3 2 w = 0 on. Find the domain of
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UMDMATH 140GulickFall

MATH 140 Midterm: Complete and Comprehensive 60 Page Midterm Exam Study Guide

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UMDMATH 140GulickFall

MATH 140 Lecture 35: Bounded Areas

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Math140 lecture 35 area of bounded regions. = l n b c n (bc) l n a l n ( ) l o o o. Find the domains of the following logarithms: o o o o n (x l n ( l
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UMDMATH 140GulickFall

MATH 140 Lecture 34: Area Revisited

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= l dx f (x) f(x) an x dx t. Recall: if the area between the graph and the x -axis. Next, let f , g be continuous on [a, b]. Then the area of the bound
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UMDMATH 140GulickFall

MATH 140 Lecture 33: Logarithmic Differentiation

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The fundamental theorem of calculus states that: G( x)= x a f (t )dt , a x b g"( x)=f (x) if f is continuous on [a, b]. If h and k are differentiable o
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UMDMATH 140GulickFall

MATH 140 Lecture Notes - Lecture 32: Negative Number, Scilab

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=g (f (x))=[g"( f (x))] f "( x)=g(f ( x)) g(f ( x))f "( x) dx= g(u) du=g (u)+c=g ( f ( x))+c: substitute u, then substitute f(x) for u. Examples: ex1:
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UMDMATH 140GulickFall

MATH 140 Lecture 31: Indefinite Integrals

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If f is any antiderivative of f on [a, b], then b a f ( x) dx=f (b) f (a: the big deal in evaluating b a f ( x) dx is finding an antiderivative of f, n
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UMDMATH 140GulickFall

MATH 140 Lecture Notes - Lecture 30: Mean Value Theorem, Antiderivative

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0 sin x dx with riemann sums: to prepare for the fundamental theorem, let f be continuous on [a, b], define g( x)= x a f (t )dt for all x in [a, b], no
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UMDMATH 140GulickFall

MATH 140 Lecture 29: Integral Properties

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U f ( p)=f (c) h+f (c+h)h+f (c+2h)h+ +f ( c+(n 1)h) h. Lf ( p)=f (c+h) h+f (c +2h) h+ f ( c+h)h o o o: properties of area: A small< alarge o o o: riema
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UMDMATH 140GulickFall

MATH 140 Lecture Notes - Lecture 28: Riemann Sum, If And Only If

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A smaller< a larger o o o: lower and upper sums: U f ( p)= m1(x1 x0)+ m n(xn xn 1) o o: note: lf ( p) u f (p, partitions, let p be a partition by addin
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UMDMATH 140GulickFall

MATH 140 Lecture Notes - Lecture 27: Axa, Royal Institute Of Technology

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UMDMATH 140GulickFall

MATH 140 Lecture Notes - Lecture 25: Inflection Point, Inflection

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= 0 for all x in the domain: symmetry with respect to the origin, occurs when f ( ) (x) x = f for all x in the domain. For all examples, find relative
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UMDMATH 140GulickFall

MATH 140 Lecture Notes - Lecture 23: Inflection, Second Derivative

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The graph of f is concave upward on an interval i if f " is increasing on i . The graph of f is concave downward on an interval i if f " is decreasing
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UMDMATH 140GulickFall

MATH 140 Lecture Notes - Lecture 24: Asymptote, Inflection

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Relative extreme values are values of the function (ex: f (a)) Inflection points are points of the form ( c , f ( c )) Be sure to label the axes on the
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UMDMATH 140GulickFall

MATH 140 Lecture Notes - Lecture 26: Mean Value Theorem, Inflection

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The following material will be covered by the exam: max-min problems, methods for solving them: Use section 4. 1 (plugging in critical points) Second-d
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UMDMATH 140GulickFall

MATH 140 Lecture 22: More Applications

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Problems: find two nonnegative numbers whose sum is 1 and such that the product of the square of one number and the cube of the other number is maximal
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UMDMATH 140GulickFall

MATH 140 Lecture Notes - Lecture 21: Aomedia Video 1, Candela, Ferrari P

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UMDMATH 140GulickFall

MATH 140 Lecture Notes - Lecture 20: Mean Value Theorem, If And Only If

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Math140 lecture 20 finding relative extrema. Mean value theorem: let f be continuous on [a, b] and let f " exist on (a, b). Then there is a c in (a, b)
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UMDMATH 140GulickFall

MATH 140 Lecture Notes - Lecture 19: Exponential Decay, Exponential Growth

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UMDMATH 140GulickFall

MATH 140 Lecture 18: Antiderivatives

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UMDMATH 140GulickFall

MATH 140 Lecture Notes - Lecture 17: Cosc, Mean Value Theorem

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Then there is a c on (a, b) such that f " (c)= f (b) f (a) b a: three star theorem. It says that the slope of the tangent line at (c, f(c)) = the slope
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UMDMATH 140GulickFall

MATH 140 Lecture 16: Graphing Problems Involving Derivatives

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Then f(x0) = maximum value for all x in [a, b]. for all x in [a, b]; it is the minimum if f (x) f (x0) f ( x) f (x0) if f (x0) is an extreme value if i
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UMDMATH 140GulickFall

MATH 140 Lecture Notes - Lecture 15: Paper Cup, Airco Dh.2, Quotient Rule

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E4 a: quotient rule: f " ( x)= = y ex e y x ex+ex: plug point in: dy dx. 0e1+e0 = 1 e: equation of the line: y 1=( 1 e)(x, justify why the equation ln
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UMDMATH 140GulickFall

MATH 140 Lecture Notes - Lecture 14: Stol, Triangular Prism, Pythagorean Theorem

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UMDMATH 140GulickFall

MATH 140 Lecture Notes - Lecture 13: Ellipse, Pythagorean Theorem

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UMDMATH 140GulickFall

MATH 140 Lecture 11: Chain Rule

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UMDMATH 140GulickFall

MATH 140 Lecture Notes - Lecture 12: Quotient Rule, Differentiable Function

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Examples of implicitly defined functions: o o x2+ y2=4 exy+x2 y3= . =0: derive: 2x+2y dy dx, solve for dy/dx: 2y dy dx. = x y: thus, dy dx at ( 1, )= 1
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UMDMATH 140GulickFall

MATH 140 Lecture Notes - Lecture 10: Quotient Rule, Fax, Third Derivative

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UMDMATH 140GulickFall

MATH 140 Lecture Notes - Lecture 9: Quotient Rule, Product Rule

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UMDMATH 140GulickFall

MATH 140 Lecture Notes - Lecture 8: Power Rule, Differentiable Function, If And Only If

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Definition of the derivative f " (a)=lim x a f ( x) f (a) x a =lim h 0 f ( a+h) f (a) h: for a general x in the domain: f (t ) f (x) t x lim t x. If a
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UMDMATH 140GulickFall

MATH 140 Lecture 6: Bisection Method and Derivatives

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If f(c1) > 0, then let a point c2 be the midpoint of a and c1: ex 1: let f ( x)=cos x x . Approximate the zero of f to within 1/8. o o o o f (0)=cos0 0
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UMDMATH 140GulickFall

MATH 140 Lecture Notes - Lecture 7: Write-Off, Umber, Intermediate Value Theorem

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Sample exam problems and solutions: problem 1: determine which of the limits below exist as a number, which as , which as , and which do not exist. Fin
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UMDMATH 140GulickFall

MATH 140 Lecture 5: Continuity and the I.V.T.

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Math140 lecture 5 continuity and the intermediate value theorem. +n for all n, it is continuous at all x in its domain: a function f is continuous if i
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UMDMATH 140GulickFall

MATH 140 Lecture 4: One-Sided Limites

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Math140 lecture 4 one-sided and infinite limits. Let f (x)=c lim x a and let g( x)=l lim y c. , then g( f (x))=l lim x a: note: as x goes to a, then y
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UMDMATH 140GulickFall

MATH 140 Lecture Notes - Lecture 1: Quadratic Formula, Polynomial, Trigonometry

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UMDMATH 140GulickFall

MATH 140 Lecture Notes - Lecture 3: Quotient Rule, Product Rule

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Math 140 lecture 3 limits (continued) = l if for each a > 0 there is a > 0 so that if 0 < |x-a| < , then |f(x)-l| < : show that, let > 0 arbitrary. To
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UMDMATH 140GulickFall

MATH 140 Lecture Notes - Lecture 2: Farad, Fot, Constant Function

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UMDMATH 140GulickFall

MATH 140 Lecture Notes - Lecture 38: Ellipse, Hyperbola

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Math140 lecture 38 conic sections (cont. ) Let p 1 and p 2 be distinct points in the plane. Let | p 1 p 2 | > 2 a , where a is a positive. The points p
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UMDMATH 140GulickFall

MATH 140 Lecture 35: Bounded Areas

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Math140 lecture 35 area of bounded regions. = l n b c n (bc) l n a l n ( ) l o o o. Find the domains of the following logarithms: o o o o n (x l n ( l
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UMDMATH 140GulickFall

MATH 140 Lecture 36: Exam 4 Review

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( 1 + 2 1 = 0 (2. Explain: since ln x is increasing on [1, 2], the left sum is automatically less than n x dx l. 2 w w3 2 w = 0 on. Find the domain of
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UMDMATH 140Nathaniel ManningFall

MATH 140 Lecture 29: 5.4 - The Fundamental Theorem of Calculus

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UMDMATH 140GulickFall

MATH 140 Lecture Notes - Lecture 37: Ellipse

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Math140 lecture 37 conic sections (parabolas and ellipses) Let p be a point not on a given line l . P and l form a parabola: let p = (0, c , let the li
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UMDMATH 140GulickFall

MATH 140 Lecture Notes - Lecture 8: Power Rule, Differentiable Function, If And Only If

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Definition of the derivative f " (a)=lim x a f ( x) f (a) x a =lim h 0 f ( a+h) f (a) h: for a general x in the domain: f (t ) f (x) t x lim t x. If a
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UMDMATH 140GulickFall

MATH 140 Lecture Notes - Lecture 17: Mean Value Theorem

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UMDMATH 140Denny GulickFall

MATH 140 Lecture Notes - Lecture 19: Exponential Decay, Exponential Growth

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UMDMATH 140GulickFall

MATH 140 Lecture 31: Indefinite Integrals

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If f is any antiderivative of f on [a, b], then b a f ( x) dx=f (b) f (a: the big deal in evaluating b a f ( x) dx is finding an antiderivative of f, n
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UMDMATH 140GulickFall

MATH 140 Lecture Notes - Lecture 27: Axa, Royal Institute Of Technology

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UMDMATH 140Denny GulickFall

MATH 140 Study Guide - Quiz Guide: Intermediate Value Theorem, Write-Off, Asymptote

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Sample exam problems and solutions: problem 1: determine which of the limits below exist as a number, which as , which as , and which do not exist. Fin
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UMDMATH 140GulickFall

MATH 140 Study Guide - Final Guide: Cosc, Paq, Paper Cup

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UMDMATH 140GulickFall

MATH 140- Final Exam Guide - Comprehensive Notes for the exam ( 76 pages long!)

OC237612176 Page
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Math 140 lecture 1 precalculus review and limits. Quadratic formula: ex: (cid:884)(cid:2871) (cid:885)(cid:2870) =(cid:882) (cid:1858) =(cid:882, = (ci
View Document
UMDMATH 140GulickFall

MATH 140 Lecture Notes - Lecture 38: Ellipse, Hyperbola

OC5374883 Page
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Math140 lecture 38 conic sections (cont. ) Let p 1 and p 2 be distinct points in the plane. Let | p 1 p 2 | > 2 a , where a is a positive. The points p
View Document
UMDMATH 140GulickFall

MATH 140 Midterm: Complete and Comprehensive 60 Page Midterm Exam Study Guide

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UMDMATH 140GulickFall

MATH 140- Midterm Exam Guide - Comprehensive Notes for the exam ( 76 pages long!)

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Math 140 lecture 1 precalculus review and limits. Quadratic formula: ex: (cid:884)(cid:2871) (cid:885)(cid:2870) =(cid:882) (cid:1858) =(cid:882, = (ci
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UMDMATH 140allFall

MATH 140 Final: MATH140 Final Exam 2010 Fall

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UMDMATH 140GulickFall

MATH 140 Lecture 35: Bounded Areas

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Math140 lecture 35 area of bounded regions. = l n b c n (bc) l n a l n ( ) l o o o. Find the domains of the following logarithms: o o o o n (x l n ( l
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UMDMATH 140allFall

MATH 140 Study Guide - Final Guide: Cubic Foot

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UMDMATH 140GulickFall

MATH 140 Lecture 36: Exam 4 Review

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( 1 + 2 1 = 0 (2. Explain: since ln x is increasing on [1, 2], the left sum is automatically less than n x dx l. 2 w w3 2 w = 0 on. Find the domain of
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