Consider the function defined by f(x) = log; (2x + 1). %3D Determine the its interval of convergence.

Q: Does / dx converge or diverge? Justify. -7 0, x' + x'

A: Plot the graph of the function.

Q: Find the radius of convergence for: 3" n=D1

A: We have to find the radius of convergence

Q: 1 E(-1)"+1, ( n + 1 ) . 3η n=1

A: To find whether converges or diverges

Q: 1 dx (x + 1)2 -2

A: We have to determine whether  ∫-2o{1/(x+1)2 }dx  is convergent or divergent.  Let I =  ∫-2o{1/(x+1)2…

Q: f(x) = log5 (2x + 1).

A: To  Determine:  Interval of convergence  f ( x ) = log5 ( 2x +1)

Q: Use the Comparison Test to determine whether or not the integral converges.

A: If f(x)≥g(x)≥0 on the interval [a,∞) then, If ∫a∞f(x)dx converges then so does∫a∞g(x)dx. If…

Q: dx converges. Determine the values of p for which

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Q: 1 dx x² +7

A:

Q: Find 2x dx. x2-4 (if it converges)

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Q: f(x) x² + 3

A: Consider the function fx=x4x2+3 Here, the objective is to find the convergence range of the…

Q: Find the radius of convergence as n goes to infinity of (log n)2 xn.

A: The given series is                                     ∑n=0∞log n2xn

Q: Examine the convergence of ,where a>1. (log x)" +1

A: First I have told about Improper integral of first kind and then using it evaluate the given…

Q: Given f (x) = a² – x – 6.Using the fixed point iteration method (x=g(x)), where g(x) is a negative…

A: Given: The function fx=x2-x-6.

Q: Use the definition to show that dx 2x2 converges.

A: We have to show that the given integration converges.…

Q: 1 -dx xln*x 1.

A: To determine if the following is a convergent or divergent. ∫e∞1xln4xdx Solution: A indefinite…

Q: 1 x + ex 2 g dx

A:

Q: Q1 Determine if the following integral converges or diverges : 1 ¡ -dx . (2x-1)³ -00

A:

Q: Find R and the Interval of Convergence o (-1)" (x)" 272

A: Given problem:-

Q: 2) is E=1 2n convergent?

A:

Q: Find an example of fn → f in measure, but for every x, fn(x) does not converge to f(x).

A: We have to find an example of fn→f in measure, but for every x, fn(x) does not converge to f(x).

Q: 51. For which values of a does eax dx converge?

A:

Q: For what values of p does xP dx converge?

A: Convergence and Divergence: When the limit exists and its value is a finite number then it is known…

Q: Does sin () x 7 converge or diverge? Why?

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Q: use the Comparison Test to determine whether or not the integral converges.

A:

Q: Q6. (i) Given Iog(itt) = tE+ t'-t"+ -.., valid for IEl<1, determine the power serhes for log (+2x )…

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Q: Use the power representation of             f(x) = 4/(1-x^2) to find its interval of convergence

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Q: f(x) = S n=1 (7-2x)" 6n

A: Radius of convergence of the Power Series : Consider the power series                ∑n=1∞ an(x-a)n…

Q: The value of the radius of convergence (R) for the function f(x) = In(5- x) will be

A:

Q: Find the interval of convergence of E n(x – 8)" n=2

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Q: 4. Which comparison would show that dx converges? x + e*

A: According to the given information, it is required to tell which comparison would show that the…

Q: 10. (x- 3)" Ln=1 n

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Q: 2x – x° dx (x – 1)° (x² + 1) 8.

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Q: dx. /1+x5 51.

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Q: +00 3 E(-1)"+1, n n=1

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Q: ax Examine the convergence of , where a>1. x (log xy" +1

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Q: Let g(x) = E-o (-1)" (2n): Find the interval of convergence g.

A: We have given g(x).  We have to find the interval of convergence.

Q: SOLVE STEP BY STEP IN DIGITAL FORMAT For what range of positive values of x is Σ 1/(1+x″) a)…

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Q: Find f xln(x +1)dx

A: ∫x ln(x+1) dx =∫ddxx22 ln(x+1) dx and by IBP: ∫uv'=uv-∫u'v =x22 ln(x+1)-∫x22ddxln(x+1) dx =x22…

Q: fn (x) = e-na", E = [1, 0)

A:

Q: Add cx to both sides and devide the equation by c to obtain g(x): x + 2x – 3 = 0 (a) For what c is…

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Q: X° +4x dx x* +3x² +2 4 2 1

A: Topic :- Integration If the limit exists as a real number, then the simple improper integral is…

Q: Is the given statement true or false? Radius of convergence of the function f(x)=ex is 1 .

A: False Solution  written below

Q: Ln=0*

A:

Q: 11 dx Determine whether is convergent or not. (3 – x)2/3

A: As the value of Integral is finite, it converges.

Q: Give an example of a sequence of continuous functions: fn : [0, 1] → R that has no pointwise…

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Q: The integral 1 dx is convergent x1.10 Select one: True False

A: We have to check

Q: Does fn converges to L1 and L2 i.e the distance between fn and f goes to 0

A: By the theorem: A metric  on BE is the uniform metric du  . A sequence of bounded functions fn:E→ℝ…

Q: (b) Explain why the integral e- *x* dx is convergent.

A:

Q: Perform a test to determine if dx converges or diverges. - 0o Vx° +6

A:

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.