Calculus Ch1-Ch2 Exam Outline

CALCULUS CH1-CH2 EXAM OUTLINE

Apply and simplify the difference quotient

Find the inverse of a function and show that it is correct using the composition of functions

Apply the properties of logarithms to simplify an expression

Solve an exponential equation

Solve a trigonometric equation

Find the average rate of change

Find the slope of a curve at a given x value

Use a graph to evaluate the limit

Apply the limit laws

Determine a one sided limit

Calculate limit (division by zero, at infinity, factoring, simplifying complex fraction, rationalizing, dividing by highest exponent)

Determine whether a piecewise function is continuous

Find the value, c, that makes a piecewise function continuous

Given a function determine intervals that are continuous

Delta – epsilon – from a graph and the full blown proof

CALCULUS CH3 EXAM OUTLINE

Find the equation of the tangent line

Graph a function and its tangent line

Calculate the derivative and evaluate at a point

Given the graph of a function, identify the graph of the derivative

Given the graph of a function, identify where the function is/is not differentiable

Calculate the derivative using the product rule, quotient rule, chain rule, of trig functions, inverse trig functions, ln, exponentials, implicit, logarithmic differentiation

Calculate the second derivative

Related rates

CALCULUS CH4 EXAM OUTLINE

Find all critical points of a function

Given characteristics of f’(x) and f”(x), identify the graph of the function

Given the graph of f’(x) and f’”(x), sketch a graph of f(x)

Given characteristics of f(x), f’(x), and f”(x), sketch f(x)

Optimization problems

Apply the mean value theorem

Apply L’Hopital’s Rule (all indeterminate forms)

Find the antiderivative of exponential, polynomial, ln, inverse trig

Solve initial value problem

CALCULUS CH5 EXAM OUTLINE

Use Riemann sums to approximate the area under a curve

Evaluate a definite integral

Find the area under a curve

Find the average value of a function

Apply the mean value thm for integrals

Integrate an indefinite integral

U substitution

Integrate trig functions, inverse trig, exponential, ln, polynomials

CALCULUS CH6 EXAM OUTLINE

Given velocity and initial position, find s(t)

Given acceleration, initial velocity, and initial position, find s(t)

Find the area between two curves

Find the volume of a solid generated by revolving a region around the x axis, the y axis, x = pos number, x= neg number, y= pos number, y=neg number using shells, disks, or washers

Applications – springs, pumping water out of a tank, lifiting problems