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

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Published on 15 Sep 2018

School

Department

Course

Professor

Miami University

MTH 151

Calculus I

Winter 2018

Final Exam

Exam Guide

Part 1 of 2

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

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

## 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.