# MATH 265 TEST 1 Review

**1.1-1.2** (considered review) Know the definition of
a function. Be able to

interpret the function if it is given algebraically, numerically or graphically .

Review **piecewise given functions** and basic function properties such as

symmetries, even and odd properties, and increasing and decreasing

properties. Review function transformations and know their effect on the

graph of a function . Understand the composition of functions. Know the

properties of the following families of functions: linear functions , power

functions, polynomial functions , rational functions and trigonometric

functions.

**1.3** Know the intuitive definition of the limit of a function at a point
a. Be

able to find **limits graphically and numerically**. Be able to find right
and

left limits of a function at a given point.

**1.4** Be familiar with the various limit laws. Be able to apply them to a

specific limit calculation . Know the ** algebraic techniques ** that help to
find

limits. Know and be able apply the **Squeeze **theorem.

**1.5** Know and understand the **definition** of continuity of a function
for

both a point a and for and interval [a,b] (remember the 3 conditions). Be

able to decide if a function is continuous if the graph or the formula of the

function is given. Be familiar with the Theorems that follow from the limit

laws . Know how to use continuity to evaluate limits (we called it the

substitution property ). Be able to determine the points where a function has

**discontinuities** and if the discontinuity is removable, be able to remove
it.

Know and be able apply the Intermediate Value Theorem to determine if

a function has roots in a given interval.

1.6 Be able to find **limits involving infinity**. Know the intuitive
definition

of the **limit of a function** at infinity. Be able to find such limits

algebraically, graphically and numerically. Know what a **vertical and a**

horizontal asymptote of a function are and how to find them using limits.

Know how to graph polynomial and rational functions using these limits and

asymptotes.

2.1 Know the **definition of the derivative **and be able** **to find
derivatives

using the definition. Be able to compute average and instantaneous rates of

change and know the difference between the two. Be able to find the

equation of the tangent line at a given point. Understand the meaning of the

derivative at a point and as a function and be able to interpret derivatives in

the context of real world applications.

2.2 Know what it means for a **function to be differentiable **at a point

and over an interval. Be able to determine points or intervals where a

function is not differentiable and be able to give justify why the function is

not differentiable. Be able to draw graphs of derivative functions from

the graph of a function. Understand the definition for higher order

derivatives.

2.3 Know the **basic rules for derivatives ** and be able to apply them to

find derivatives of given functions.

Prev | Next |