MTH 151 Study Guide - Final Guide: Rational Number, David Jude Jolicoeur, Algebraic Function

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Published on 15 Sep 2018
Department
Course
Professor
Miami University
MTH 151
Calculus I
Winter 2018
Final Exam
Exam Guide
Part 1 of 2
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Table of Contents:
Part 1:
Chapter 2
Section 2.1 Tangent Lines
Section 2.2 Definitions and Theorems
Section 2.3 Limit Laws
Section 2.4: Limit definition
Section 2.5: Continuity
Section 2.6: Limits at Infinity and Horizontal Asymptotes
Section 2.7: The derivative at a Point
Section 2.8: The Derivatives as a Function
Chapter 3
Section 3.1: Derivatives of Polynomials and Exponential Functions
Section 3.2: Product and Quotient Rule
Section 3.3: Derivatives of Trigonometric Functions
Section 3.4: The Chain Rule
Section 3.5: Implicit Differentiation
Section 3.6: Logarithmic Differentiation
Section 3.9: Related Rates
Part 2:
Section 3.10: Linearization and Differentials
Section 3.8: Exponential Growth + Decay
Chapter 4
Section 4.1: Fermat’s Theorem
Section 4.2: Rolle’s Theorem and The Mean Value Theorem
Section 4.3
Section 4.7 Optimization
Section 4:4 Indeterminant Forms
Section 4.5: Curve Sketching
Section 4.9: Antiderivatives
Chapter 5
Section 5.1: Area Problem
Section 5.3: Fundamental Theorem of Calculus
Section 5.2: Definite Integral
Section 5.4: Indefinite Integral
Section 5.5 Substitution
Section 5.4: Net Change Theorem
Chapter 6
Section 6.1: Areas between Curves
Section 6.2: Volumes
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Chapter 2
Section 2.1 Tangent Lines
A tangent line at a point is a line that has the same direction as the curve at the point of
contact
GOAL: know the slope, m, of the tangent line
Point slope: y-y1=m(x-x1)
-(x1,y1) is a point on the line
-m is the slope
Slope: two points on the line (x1, y1), (x2, y2)
M=y2-y1/x2-x1
Approximate the slope indirectly if only one point is shown on the tangent line using the
secant line because if we know 2 points on the secant line, we can get a close enough
slope of the tangent line.
From the slope of the secant line, we can get approximate slope of tangent line
Example 1)
Find an equation of the tangent line to the parabola y=x2 at the point (1,1)
Need 2 things
1) Slope=?
2) point (x,y) we know is (1,1)
For an input X, the slope of a secant line formed by points (x,x2) and (1,1) the slope or
mpq= x2-1/x-1
We are going to guess slope of the tangent line by taking x values on the left and right of
1 and placing them in a chart as shown below
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Document Summary

E(cid:272)tio(cid:374) 4. (cid:1006): olle(cid:859)s theore(cid:373) a(cid:374)d the mea(cid:374) value theore(cid:373) A tangent line at a point is a line that has the same direction as the curve at the point of contact. Goal: know the slope, m, of the tangent line. Slope: two points on the line (x1, y1), (x2, y2) Approximate the slope indirectly if only one point is shown on the tangent line using the secant line because if we know 2 points on the secant line, we can get a close enough slope of the tangent line. From the slope of the secant line, we can get approximate slope of tangent line. Find an equation of the tangent line to the parabola y=x2 at the point (1,1) Need 2 things: slope=, point (x,y) we know is (1,1) For an input x, the slope of a secant line formed by points (x,x2) and (1,1) the slope or mpq= x2-1/x-1.

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