# Textbook Notes for MATH241 at University of Delaware (UD)

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## MATH241 Lecture 27: Optimization Problems

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Steps in solving optimization problems: understand the problem, draw a diagram. Introduce notation: express the quantity to be optimized in terms of th
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## MATH241 Lecture 21: Related Rates

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If two functions are related by an equation, then their derivatives are also going to be related. The general approach is to compute the rate of change
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## MATH241 Lecture Notes - Lecture 25: Horse Length

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Math241 - lecture 25 - exam 2 review. #7) use linear approximation to estimate the value of 3. 9. L (x) = f (a) + f (a) (x f (x) = x 2. 2 4 = 4 f (4) =
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## MATH241 Lecture Notes - Lecture 24: Intermediate Value Theorem

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Math241 - lecture 24 - maximum and minimum values, and the mean value theorem. Find the extreme values of f f (x) = 2. Os x c x = 3 (find the critical
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## MATH241 Lecture Notes - Lecture 22: Hyperbola, Even And Odd Functions, Quotient Rule

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Math241 - lecture 22 - linear approximations and hyperbolic functions. The tangent line to a function y = f (x) approximate or estimate the value for a
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## MATH241 Lecture Notes - Lecture 28: Power Rule, Antiderivative

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Math241 - lecture 28 - optimization problems and antidifferentiation. A can of soda must have a capacity of. 3 and the shape of a right circular cylind
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## MATH241 Lecture Notes - Lecture 26: Inflection Point, Maxima And Minima

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Math241 - lecture 26 - derivatives and the shape of a graph. 4. 3: derivatives and the shape of a graph. If f (x) > 0 f (x) < 0 on an interval then on
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## MATH241 Lecture Notes - Lecture 14: Product Rule, Quotient Rule, Trigonometric Functions

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Math241 - lecture 14 - derivatives of trigonometric functions. 0 sin = 1 sin = 1 cos 1 = 0. C) lim sin6x x 0 6x sin4x x tanx x 0 3x. B) lim x 0 sin4x =
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## MATH241 Lecture 20: Exponential Growth and Decay (continued)

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Math241 - lecture 20 - exponential growth and decay (continued) Let initial mass of a radioactive isotope mass remaining at time t. The relative decay
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## MATH241 Lecture Notes - Lecture 18: Trigonometric Functions

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Math241 - lecture 18 - derivatives of inverse trigonometric functions and logarithmic. Use implicit: cos2 + sin2 = 1 y y y = = x (cos y) y = 1 y = 1 co
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## MATH241 Lecture Notes - Lecture 16: Power Rule

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Math241 - lecture 16 - 3. 4: the chain rule (continued) 3. 4: the chain rule (continued: the chain rule can be combined with the product and quotient r
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## MATH241 Lecture Notes - Lecture 17: Implicit Function

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Express one variable in terms of the other variable (x) y = f y = 3x2 + e5x y = x3 + 4 + t an2x. The variables are defined in terms of an equation such
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## MATH241 Lecture Notes - Lecture 19: Relative Growth Rate

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Math241 - lecture 19 - derivatives and exponential growth and decay. Case i: constant base with a variable exponent. Let y = bx y = eln bx y = ex ln b
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## MATH241 Lecture Notes - Lecture 12: Indeterminate Form

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Math241 - lecture 12 - midterm exam 1 review. = lim h 0 f(x + h) f(x) h. 4 (x + h) 4 x h h 0 ( 4 (x + h) (4 x) 4 x h 4 x h ( 4 x 4 x ( 4 x h 4 x) h. 4
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## MATH241 Lecture Notes - Lecture 13: Quotient Rule, Power Rule, Product Rule

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Math241 - lecture 13 - derivaties of polynomials and exponential functions, and product and quotient rules. 3. 1: derivatives of polynomials and expone
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## MATH241 Lecture Notes - Lecture 9: Coefficient, Tangent

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Math241 - lecture 9 - limits and derivatives. Find the vertical and horizontal asymptotes of g( = -1 is a candidate for a vertical asymptote because g(
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## MATH241 Lecture Notes - Lecture 4: Logarithm

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Math241 - lecture 4 - limit of a function and calculating limits. A limit does not exist if the function values get very large in magnitude, that is (x
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## MATH241 Lecture Notes - Lecture 11: Polynomial, Power Rule, Exponential Function

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Math241 - lecture 11 - derivatives of a polynomial *not on midterm* D) f f f f (x) (x) (x) (x) (constant) A) f(x + h) f(x) h c c h (x) = lim h 0 lim h
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## MATH241 Lecture 6: Continuity

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*note the requirements: if a lim x a f (x) 2. f (a) lim x a is defined f exists (x: they are equal is continuous at the given point. = s in f 6 (x) lim
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## MATH241 Lecture Notes - Lecture 10: Differentiable Function

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Math241 - lecture 10 - derivatives and differentiable functions. 3 x + 3x h + 3x h + h + 2x + 4xh + 2h x 2x. 3x h + 3xh + h + 4xh + 2h. 3x + 3xh + h +
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## MATH241 Lecture Notes - Lecture 7: Intermediate Value Theorem, Asymptote, Polynomial

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Math241 - lecture 7 - continuity and limits at infinity. The intermediate value theorem : suppose that f f (b) and let and where in n be any number bet
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## MATH241 Lecture Notes - Lecture 8: Blood Vessel

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Math241 - lecture 8 - derivatives and rates of change. An alternative for the expression for the slope of the tangent line is obtained if we consider a
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## MATH241 Lecture Notes - Lecture 3: Sign Function, Piecewise

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UDMATH241hassanFall

## MATH241 Chapter 3: Section: 3.1-3.2

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## MATH241 Chapter Notes - Chapter 4: Fendi

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## MATH241 Chapter 3: Section 3.3

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## MATH241 Chapter 2.7: Rates and Derivative

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## MATH241 Chapter 3.6-3.7: Chapter 3

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## MATH241 Chapter 3: Chain Rule

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## MATH241 Chapter 4: Anti-Deriv

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## MATH241 Chapter 3: Related Rates

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## MATH241 Chapter 3: Implicit

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## MATH241 Chapter 1: Functions and Models

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## MATH241 Chapter 5: 5.4 notes

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## MATH241 Chapter 3: Section 3.5: Chain Rule

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