Use integration, the Direct Comparison Test, or the Limit Comparison Test to test the integral for convergence. If r than one method applies, use whatever method you prefer. In 5 0 6x 。 -2 -6/x e dx Select the correct choice below and fill in the answer box to complete your choice. (Type an exact answer.) OA. The integral converges because OB. The integral diverges because In 5 0 In 5 0 - 6/x 6x 2e -2-6/x 6x .... dx = dx =

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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**Transcription for Educational Website**

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**Convergence Test for Integral**

Use integration, the Direct Comparison Test, or the Limit Comparison Test to test the integral for convergence. If more than one method applies, use whatever method you prefer.

\[ \int_{0}^{\ln 5} 6x^{-2} e^{-6/x} \, dx \]

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**Multiple Choice Question**

Select the correct choice below and fill in the answer box to complete your choice. (Type an exact answer.)

- **A.** The integral converges because 

  \[ \int_{0}^{\ln 5} 6x^{-2} e^{-6/x} \, dx = \, \_\_ \]

- **B.** The integral diverges because 

  \[ \int_{0}^{\ln 5} 6x^{-2} e^{-6/x} \, dx = \, \_\_ \]

--- 

**Instructions for Students:** Analyze the integral using your preferred method of convergence testing. Provide the final answer in the space provided.
Transcribed Image Text:**Transcription for Educational Website** --- **Convergence Test for Integral** Use integration, the Direct Comparison Test, or the Limit Comparison Test to test the integral for convergence. If more than one method applies, use whatever method you prefer. \[ \int_{0}^{\ln 5} 6x^{-2} e^{-6/x} \, dx \] --- **Multiple Choice Question** Select the correct choice below and fill in the answer box to complete your choice. (Type an exact answer.) - **A.** The integral converges because \[ \int_{0}^{\ln 5} 6x^{-2} e^{-6/x} \, dx = \, \_\_ \] - **B.** The integral diverges because \[ \int_{0}^{\ln 5} 6x^{-2} e^{-6/x} \, dx = \, \_\_ \] --- **Instructions for Students:** Analyze the integral using your preferred method of convergence testing. Provide the final answer in the space provided.
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