Calculus II/Test 1

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Wright State University Lake Campus/2017-1/MTH2310

  • The four midterm tests are on 2/2/17, 3/9/17, 3/30/17, and 4/20/17 (all Thursdays) from 11:30 - 12:50 pm.
  • The final exam is on Monday 4/24/17, at 3:15-5:15 pm.

T1=Test 1 (sections): 1.7, 4.5, 5.6, G,, 5.7, 5.10

For each equation, solve the problem in your private wiki and generate a variation using the Prob. provided.


Parametric equation Sec 1.7 p72[edit]

Prob.[edit]

Write this parametric equation in the form y=f(x), and sketch the graph:

and

Limits Sec 4.5 p290[edit]

Prob.[edit]

Evaluate the limit:

Prob.[edit]

Evaluate the limit: (see page 297 problem 47)

solution

Let

This is correct, but we need

  • Because a reasonable person might forget to take antilog in the last step, the tests will not be multiple choice, but instead graded for partial credit.

Similar problem:

See Example 8 Sec 4.5

Integration by parts Sec 5.6 p283[edit]

Prob.[edit]

Evaluate

sample alternative: : this was hard. we do integration by parts and solve 2 equations in two unknowns.

http://www.petervis.com/mathematics/integration_by_parts/integrate_e_x_sinx.html

Prob.[edit]

Evaluate

hint: https://www.youtube.com/watch?v=htTerwAGeLY
hint

This one does :

. Now let

I think

Also, the derivative of the arcsin should be obtained using this trick:

Prob.[edit]

hint- see also p.389 in textbook

Do the second term with the substitution:

This should lead to: ∫ [cos(x) - cos(x)*sin(x)^2] dx = sin(x) - (1/3)sin(x)^3 + c

Partial Fractions Sec 5.7 p398[edit]

Probs.[edit]

  • Section 5.7 (pp. 389-392): Examples 1, 2, and 4. You need not memorize the half-angle formulas.

Improper Integrals Sec 5.10 p413[edit]

Probs.[edit]

  • I think I did examples 2 and 4 pp416-417
  • Example 3 involves the arctan, which is the integral of 1/(1+x2), which I consider a low priority integral to memorize. Good project, if you show why.

Probs[edit]

  • Time permitting, we will look at a "type 2" case: Example 9 is fun, because it uses the Comparison Theorem. But you need to be certain that you understand this theorem.