Review for Exam 1

Exam rules

No notes or books nor cell phones are allowed. You are allowed to have a calculator, but not one that can do calculus. A scientific calculator is fine (that can do logs, exponentials, sines, sqrts, etc.).

You have the full period to work on it. When you are finished, you can give me your exam and leave.

Format

Questions will be similar to daily homework questions and weekly assignment questions.

You must show your work. For example, if you need to evaluate a definite integral, you must derive the antiderivative and express how you evaluate it.

Topics

From Calculus 1

Limit Definition of the Derivative (and other important definitions)

Tangent lines

Absolute max/min (and tests for)

Intervals of increase/decrease and local max/min

Intervals of concavity and inflection points

Area

Volume of solids of revolution

Section 6.1: Inverse functions

One-to-one functions

Properties of inverse functions

Compute the inverse to a given function

Section 6.2: Exponential functions

Exponent properties

Compute their limits, derivatives, and integrals ( (d/(d x))((e^x))=(e^x), ∫(e^x)d x=(e^x)+C )

Section 6.3: Logarithms

Solve exponential equations

Logarithm properties

Section 6.4: Logarithm derivatives

Compute their limits, derivatives, and integrals ( (d/(d x))(ln(x))=(1/x), ∫(1/x)d x=ln(|x|)+C )

Section 6.6: Inverse trigonometry

Inverse sine, inverse cosine, and inverse tangent

Compute their limits, derivatives, and integrals ( (d/(d x))((sin^(-1))(x))=(1/(Sqrt[1-(x^2)])), (d/(d x))((cos^(-1))(x))=-(1/(Sqrt[1-(x^2)])), (d/(d x))((tan^(-1))(x))=(1/(1+(x^2))) )

Section 6.8: Indeterminate limits

L’Hopital’s rule

The different indeterminate forms

Studying

Try problems you haven’t worked from the exercises from the corresponding section of your calculus book. For those problems that ask you to use a graphing calculator, on our exam I would give you the graph.

Review the weekly assignments. Remember which ones caused you the most trouble. Find similar examples in the textbook and the posted outlines, then try similar exercises in the textbook.

Visit either me or the Math/Stats tutoring lab in MEP 457 for walk-in tutoring by upper level math/stats students with your questions.

Sample questions

Let f(x)=-3+(4^(2x-1)).

Find an equation for the tangent line to y=f(x) at x=1.

Find a formula for (f^(-1))(x).

Let g(x)=(tan^(-1))((x^2)+x)+π.

What is the domain of g(x)?

What is the range of g(x)?

Find all critical numbers for g(x) and for each determine if each produces a local maximum point, a local minimum point, or neither.

Find the area of the region bounded by y=(1/x), y=-1, and x=-2.

Show[Plot[{(1/x),-1},{x,-3,3},PlotRange->{-5,5}],Graphics[Line[{{-2,-5},{-2,5}}]],PlotRange->{-5,5}]

Find the volume of the solid obtained by rotating about the x-axis the region bounded by y=(e^(-x)) and the x-axis for 0≤x≤2.

Find the limit if it exists.

(lim_(x->0))((x-sin(x))/(x^3))

(lim_(x->(SuperPlus[0])))((((1/x)))^(sin(x)))