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Definition
| A sequence is a list of numbers. It is also a function whose domain is a subset of non-negative integers. |
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| What is the explicit formula for the general term of an arithmetic sequence? |
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Definition
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| What is the explicit formula for the general term of a geometric sequence? |
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| What is are the two ways an integral could be improper? |
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Definition
| An integral is improper if one or both of the limits of integration are infinite or if a vertical asymptote exists between the limits of integration. |
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Describe the steps for evaluating the integral:
[image] |
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Definition
1) Rewrite as the limit:
[image]
2) Evaluate the definite integral.
3) Evaluate the limit.
4) If the limit exist, the integral converges to the limit. If the limit DNE for any reason, the integral diverges. |
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Describe the steps for evaluating the integral:
[image] |
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Definition
1) Split into two integrals:
[image], where c is ANY constant (pick one).
2) Evaluate ONE of the two integrals.
3) If either of the chosen integrals diverges, then the original diverges.
If both integrals converge, then the original integral is the sum of the two convergent integrals. |
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| Describe the steps for evaluating the integral:[image] |
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Definition
1) Split the integral into two:
[image], where f(a)=0 (where the integrand has a vertical asymptote).
2) Evaluate the integrals one at a time.
3) If one of the integrals diverges, the original diverges.
If both converge, then the original converges to the sum of the two convergent integral |
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| Explain how to determine whether f(x) or g(x) grows at a faster rate. |
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Definition
1) If [image], then f(x) grows faster.
2) If [image], f(x) grows slower (g(x) grows faster).
3) If [image], f and g grow at the same rate. |
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