Summer 2022
MATH 1226 Test 2 review
NAME:
Date: 07-26-2022
Test directions
• Show reasoning that is complete and correct by the standards of this course. All answers should be
justified with work.
• Do not use techniques not taught in this course.
• The use of a calculator is not needed on this Test.
• Improper use of (or the absence of) proper notation will be penalized.
1. Given the following limit, state the type of indeterminate form that corresponds to this limit and
find the limit.. If you use L’Hospital’s Rule explain why you can use it and write an ”H” above the
equal sign when you use it.
1
1
limx→0+
−
.
x ex − 1
2. Evaluate the following integral using a trigonometric substitution. State the restriction for the angle
θ. Express the final answer in terms of the variable x.
R
√
x2
dx
9 − 25x2
3. Evaluate the following integral using the method of partial fractions. Express the final answer in
terms of the variable x.
R
4x
dx
3
2
x +x +x+1
4. Evaluate the following integral and determine whether the integral is convergent or divergent.
R3
1
dx
−2
x4
R
5. Suppose that f , f ′ , f ′′ are continuous everywhere. Evaluate xf ′′ dx and express the answer in
terms of f and f ′ .
1