Let f and g be as in the figure, we may deduce that if I g(x)dx converges then

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

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Q: 1) Does cos" cn) Sin*™(n) converges uniturmly on D, : [0, K14] ?. And on

A: Given sequence of function is, fnx=cosnxsin2nx. It can be written as, fnx=cosxsin2xn. If common…

Q: Theorem 64. Let {pk}1 converge to point If y # x, then {pk}1 does not converge to y. x.

A: Given that sequence pkk=1∞ converges to point x.

Q: WNII sin 2 7) Show that 4 VN converges/diverges.

A:

Q: 20. Show that if E-1a, converges, then 1 + sin(a,) Σ n=1 converges.

A:

Q: 00 Determine whether the improper integral ²+37+1 e dx converges or diverges. Show all your steps.

A: Since there is infinity in the upper bound, this is improper integral of type 1.   To evaluate an…

Q: Let f and g be as in the figure, we may deduce that if | g(x)dx converges then f(x)dx |4 y = g(x) v…

A: We will use the fact that the definite integral gives the area under the curve. And then we will use…

Q: Consider the sequence of functions {fn}=2 where fn: [a, b] → R defined for n 2 2 by if 0<x s -n² (x…

A: Definition: Suppose fn is a sequence of functions fn:S→ℝ and f:S→ℝ. Then fn→f pointwise on S if…

Q: Suppose fn : S → ℝ are functions that converge uniformly to f : S → ℝ. Suppose A ⊂ S.  Show that…

A: Suppose fn : S → ℝ are functions that converge uniformly to f : S → ℝ. Suppose A ⊂ S.  Show that the…

Q: Let f and g be as in the figure, we may deduce that if | g(x)dx converges then | f(x)dx a a | 4 y =…

A: Given two functions f(x) and g(x) It can be clearly seen that the area bounded by the function g(x)…

Q: dX 2) Show that ? Xe converges/diverges.

A: SOLUTION-

Q: 0o Inx dx Evaluate it and state whether it converges or diverges. x2 d)

A: That's easy. Have a good day!!!

Q: Let {fn(x)} : „x ER and > 0. 1+ nx Show that ift>0, the sequence {fn(x)} converges uniformly on

A: Given: To explain the given statement as follows, To show that if t&gt;0, the sequence fnx converges…

Q: 1 dx is convergent True 8

A: Solution is given as below:

Q: Use the root test to determine whether ye converges, where An is as follows. an =

A: Explanation of the answer is as follows

Q: Let r be a constant. Suppose >,r i=1 converges to 8, then the sum of >r' is i=0 Answer:

A:

Q: Consider the sequence {fn(x)}, where sin(nx) fn(x) = 1+ nx a. Show that fn(x) converges pointwise to…

A:

Q: 59. Show that 1- sin x dx converges. x? 00

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Q: Determine i it convergcs or dverges. Evaloate if converges oo dv 2.

A: We have given,

Q: 6+ cos (7x) Perform a test to determine if x converges. T/ 7 00 5 dx X II

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Q: 2. s) Let x1 = 1 and define rn+1 = v3+2x, for n E N. Show that the sequence (xn) converges and find…

A:

Q: Determine whether

A: Solution: Consider the given integral equation: J = ∫-11dxx1/3 Since the given integrand is defined…

Q: 1 d.x x In (ex)

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Q: If lim,- f(x)=0, then f(x)dx converges Select one: True O False

A: As the mention in above given question when x goes towards infinte than function f(x) gives 0. It…

Q: dx Determine if the improper interal S, xc Fnd it valne if it converges. Conneeges on diree jes.…

A:

Q: The sequence a, = sin (A) is unbounded (C) converges to a number less than 1 (E) diverges to…

A: Limit of a sequence

Q: determine if The fenes Converget, E Converges, fınd The fum it

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

A: Idea: use substitution method to integrate  then we get undefined value  so integral is not convert

Q: Σ Suppose that ax" converges to a function y such that y" – 2y' + y = 0 where y(0) = 0 and y'(0) =…

A:

Q: Determine if H conver or diverges. Evaluate i it ges converges dx 3

A: We have to find convergence and divergence of integral .Integral is shown as below:

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

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Q: Let 1 = S dx c+∞ 4-x I = dx Then I O converges to 3 O converges to .

A: Consider the integral: I=∫1+∞4-xx3dx

Q: d 23 a Show that dx :(-{e-*(sin x + cos x) ) = e¬* sin x. N. 00 b Find e* sin x dx, and show that…

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Q: If lim=c>0, then both convergent and both divergent. ylgn O Ihi O

A: If limn→∞anbn=c&gt;0, then ∑bn,  ∑an both convergent and both divergent. (a) True (b) false

Q: 1 -dx x In*(ex) 1. e

A: Topic = Integration If the limit exists and is a finite number, we say the improper integral…

Q: Set an where r E R is a real number. Prove that ɑn converges to 0 if (-1, 1), cônverges tó 1 if r =…

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Q: If E, 2"an converges and Eo(-1)"2"an diverges, then the radius of conver- gence of Eo anx" is 2. =0

A:

Q: IV. Determine if the given is convergent or divergent. 1. dx (x2 + 1)² 1

A:

Q: Find the interval of convergence of f(x) dx where f(x) = (-1)+1(x-6)" 8. n%3D1 n6h

A: Given that             f(x)=∑n=1∞ (-1)n+1(x-6)nn 6n ⋯⋯⋯⋯ (1) To find the interval  of convergence by…

Q: dx and state whether it converges or diverges.

A: Given that a infinite integration and we find it is converges or diverses. We know that Converse…

Q: 2n+1 4. Use the definition to prove that ) converges.

A:

Q: -4 After evaluation, Jo dx tends to be 0 x2-9 A. convergent B. divergent C. insurgent D. allegiant

A:

Q: If E, 2"an converges and E o(-1)"2"an diverges, then the radius of conver- gence of o anx" is 2.

A: According to the given information, Suppose,

Q: dx heorem 1.7.1 is convergent if and only if µ < 1. (x – a)H a

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Q: 1 ·dx (х + 1)2 -2

A:

Q: Suppose that f e C(R) and that | If(x)|dx converges. Show then that 2 f(x)| sin nx|dx sx)dx. lim n00

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Q: if 0, dx converges to 1 then c= се O a. -3 O b. 3 O c. 1 O d. -1 3 1/3

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Q: find if diverges or converges. if converges, then find its limit cos² (8n) an where n 2 0 8n-1

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Q: {au, ) IL x y² dx dy Q4-A) Show that the sequence B) Evaluate : ah (sinn)}, +sinh( converges to (1).

A: Given

Sequence and Series

A sequence is defined as a collection of things. Series is defined to sum the things one by one in the sequence.  It was invented by German mathematician Carl Friedrich Gauss.