4. Let a > 0 be a (fixed) real number. (a) Using lower and upper Riemann sums for n≥ 1, we have 1ª + 2ª +...+ (n − 1)ª ≤ "

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Q: 1) a)lim n(a (aa – 1) =?

A: Given: limn→∞na1n-1 We can write, limn→∞na1n-1=limn→∞ a1n-11n We get the indeterminate form

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A: As asked we shall solve only part (a) of the given problem.We shall use MATLAB code to do the above…

Q: 6) Use "TELESCOPE technique" to find x which is involved in INFINITE PROCESS. 1 X = 20 1 1 1 1 1 1 1…

A: 6.x=120+130+142+156+172+........

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Q: 5a) When p is a real number greater than 1, it can be shown that the improper 1 1 integral |dx…

A: Convergence of Improper Integrals at left-end point: Let us suppose that x=a be the point of…

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Q: n' (a) Ax (b) The limits a, b The function f(x) which this limit is approximating.

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Q: Express dx as a limit of left Riemann sums but do not attempt to eval- x2 uate the limit.

A: Given, ∫-11-6 5x2dx

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A: Give that: f(x)=-12, -1&lt;x&lt;012,0&lt;x&lt;1  Here L=(1+1)/2=1 Fourier  series expansion given by…

Q: 2. For f, (x³ – 3x²) dx. a) Express the integral as a limit of Riemann sums. b) Use left endpoints…

A: Given definite integral is:                          ∫-12x3-3x2dx This can be expressed as limit of…

Q: 1. Below function is defined for one period 1 10 99 X 1 10 f(x) = { -9x + 9 - 10 ≤ x < -1 - 1<x< 1…

A: hi!Thank you for your question.As per guidelines we can solve one question at a time in case of…

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A: Given that                                                 f(x)=x+2x+3  &amp;g(x)=x2+2

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Q: 10) Use the Riemann-Rectangle program to evaluate the Riemann sum for f(x) = √√x+1, −1≤ x ≤ 5, with…

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Q: 4. Let a > 0 be a (fixed) real number. S (a) Using lower and upper Riemann sums for n ≥ 1, we have…

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Q: Prove that 2 +22- -6 lim 3, tan x-3tan x lim cos(x+7/6) V2* - 2-

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Q: Express the given integral f, 2x dx as the limit of Riemann sum. a. 2x dx = lim E-(1+) G+1)* E- d.…

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Q: Q2) Discuss the continuity at x=2. When: x> 2 X = 2 x< 2 Зх + 1 f(x) = } x? + 3 %3D 2х + 1

A: Our objective is to discuss the continuity at x=2.

Q: 1. Below function is defined for one period a) b) f(x) = 1 10 --X == 9 9 X 1 -=x+ 10 9 -10 < x < -1…

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