PROBLEM 01
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(1 point) Consider the integral ∫∞02z2+3z+2dz
If the integral is divergent, type an upper-case "D". Otherwise, evaluate the integral.
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PROBLEM 02
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(1 point) Consider the integral ∫∞13ln(x)x2dx
If the integral is divergent, type an upper-case "D". Otherwise, evaluate the integral.
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PROBLEM 03
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(1 point) Consider the integral ∫918x−9−−−−−√3dx
If the integral is divergent, type an upper-case "D". Otherwise, evaluate the integral.
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PROBLEM 04
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(1 point) Use the Comparison Theorem to determine whether the following integral is convergent or divergent.
1. ∫∞11cos2(x)1+x2dx |
PROBLEM 05
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(1 point) The integral ∫∞0−4x√(1+x)dx
is improper for two reasons: the interval [0,∞] is infinite and the integrand has an infinite discontinuity at x=0. Evaluate it by expressing it as a sum of improper integrals of Type 2 and Type 1 as follows:
∫∞0−4x√(1+x)dx=∫10−4x√(1+x)dx+∫∞1−4x√(1+x)dx
If the improper integral diverges, type an upper-case "D". |
PROBLEM 06
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(1 point) (a) Find the values of p for which the following integral converges: ∫∞e1x(ln(x))pdx
Input your answer by writing it as an interval. Enter brackets or parentheses in the first and fourth blanks as appropriate, and enter the interval endpoints in the second and third blanks. Use INF and NINF (in upper-case letters) for positive and negative infinity if needed. If the improper integral diverges for all p, type an upper-case "D" in every blank.
Values of p are in the interval ,
For the values of p at which the integral converges, evaluate it. Integral = |
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(張旭微積分上下學期線上課程 |
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