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c) Converge by integral test Q.10) fxe-x dx = a) 6e-5-1 25 b) 1-6e-5 25 c)(4+1) 2$ -6e-s 25 d)-

c) Converge by integral test Q.10) fxe-x dx = a) 6e-5-1 25 b) 1-6e-5 25 c)(4+1) 2$ -6e-s 25 d)-

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.2: Graphs Of Equations
Problem 78E
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pleaseeeeeee solve question 10

**Calculus and Series Questions** **Q.1)** \(\frac{d}{dx} \left( \int_{1}^{x} t \frac{1}{t} dt \right) = \) - a) \(\frac{2}{x}\) - b) \(\frac{1}{x^2} = 1\) - c) \(\frac{1}{x^2} = 1\) - d) \(\frac{3}{x}\) **Q.2)** The integral \(\int_{1}^{\infty} x^{-p} dx\) is convergent if the values of \(p\) are: - a) (-∞, 1) - b) (-∞, 2) - c) (1, ∞) - d) (2, ∞) **Q.3)** \(\int \frac{1}{x^2 + 4x + 8} dx =\) - a) \(\frac{\tan^{-1}(\frac{x+2}{2})}{2} + C\) - b) \(\ln \lvert x+2 \rvert + C\) - c) \(\frac{e^{x^2}}{x} + C\) - d) \(\frac{2}{x^2} + C\) **For Q.4 and Q.5, if \(\sum_{n=0}^{\infty} \left( \frac{x}{2} \right)^n\), then:** **Q.4)** The radius of convergence is: - a) \(R= 1\) - b) \(R= 2\) - c) \(R= \frac{1}{2}\) - d) \(R= \frac{1}{3}\) **Q.5)** The interval of convergence is: - a) \((-2, 2] \) - b) \((-2,2) \) - c) \([-2, 2)\) - d) \([-2, 2] \) **Q.6)** Determine which of the following tests could be used to show that \(\sum_{k=1}^{\infty} \left( \
Transcribed Image Text:**Calculus and Series Questions** **Q.1)** \(\frac{d}{dx} \left( \int_{1}^{x} t \frac{1}{t} dt \right) = \) - a) \(\frac{2}{x}\) - b) \(\frac{1}{x^2} = 1\) - c) \(\frac{1}{x^2} = 1\) - d) \(\frac{3}{x}\) **Q.2)** The integral \(\int_{1}^{\infty} x^{-p} dx\) is convergent if the values of \(p\) are: - a) (-∞, 1) - b) (-∞, 2) - c) (1, ∞) - d) (2, ∞) **Q.3)** \(\int \frac{1}{x^2 + 4x + 8} dx =\) - a) \(\frac{\tan^{-1}(\frac{x+2}{2})}{2} + C\) - b) \(\ln \lvert x+2 \rvert + C\) - c) \(\frac{e^{x^2}}{x} + C\) - d) \(\frac{2}{x^2} + C\) **For Q.4 and Q.5, if \(\sum_{n=0}^{\infty} \left( \frac{x}{2} \right)^n\), then:** **Q.4)** The radius of convergence is: - a) \(R= 1\) - b) \(R= 2\) - c) \(R= \frac{1}{2}\) - d) \(R= \frac{1}{3}\) **Q.5)** The interval of convergence is: - a) \((-2, 2] \) - b) \((-2,2) \) - c) \([-2, 2)\) - d) \([-2, 2] \) **Q.6)** Determine which of the following tests could be used to show that \(\sum_{k=1}^{\infty} \left( \
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