# MTH131: Calculus With Analytic Geometry I

### Course Description

This first course in calculus presents analytic geometry and the calculus of algebraic and transcendental functions including the study of limits, derivatives, differentials and an introduction to integration.

The techniques of calculus will be used to analyze functions and their graphs, solve real-world applications, develop computational and numerical methods, and analyze the relationship between differentiation and integration using the Fundamental Theorem of Calculus.

### Course Objectives

Throughout this course, the student will learn to:

Quiz 1Â

evaluate limits of functions

state and use the epsilon-delta definition of the limit

apply the concept of continuity, including the Intermediate Value Theorem

locate asymptotes of graphs of functions

Quiz 2

use the definition of the derivative and interpret the derivative as both an instantaneous rate of change and as the slope of the tangent line to a function at a point

differentiate functions using the rules for differentiation: power, product, quotient, and chain rules

differentiate exponential, logarithmic, and trigonometric functions

Quiz 3

locate extreme values and points of inflection of graphs of functions

find and apply higher-order derivatives and understand how they relate to the graph of a function

apply Newton's Method

apply Rolle's Theorem and the Mean Value Theorem

Quiz 4

solve applied optimization problems

Quiz 5

use implicit differentiation and solve related rates problems

Quiz 6

state and use the Fundamental Theorem of Calculus

Final Exam

The final exam is a cumulative exam involving all of the sections combined.

The REVIEW link above links to a previous final exam with a solution guide.