CALCULUS REVIEW EXERCISES STAT/MATH 511
1. Compute the following limit:
lim
x→2
x2−4
x−2
2. Are there real values of xfor which f(x) = x2+ 2x+ 2 is equal to zero? Justify your
answer.
3. For a /∈ {0,−1}and θ > 0, compute the following:
Zθ
0
xadx
4. Find the derivative of f(x) = eax2+bx+c, where a,b, and care nonzero constants.
5. Compute the following:
d2
dx2xex
6. What is the sum of the infinite series
1
3+1
6+1
12 +1
24 +1
48 +···?
7. Evaluate the following double integral:
Z1
0Zx
0
2xy2dydx
8. Compute the following:
Z∞
0
xe−xdx and Z∞
0
x2e−xdx
9. Evaluate the following:
lim
x→0xexlim
x→∞ xexlim
x→0xe−xlim
x→∞ xe−x
10. Find the derivative of f(x) = x/ ln(x).
11. Compute the following limit:
lim
n→∞ 1 + 1
nn
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