x +x2+..+ xn Let 0< a is convergent, show that < b, > is convergent or divergent (2)Let is convergent, show that is convergent or divergent (3)ls there any such that , < bn > are both diverge?

Q: Evaluate the definite integral using a limit of Riemann Sums. Fill in each blank and submit your…

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Q: The shaded area of figure is best described by U B O (AUB)'u (ANB) O B' O (AUB) N (ANB) O ANB' None…

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Q: EVALUATE THE FT. 3 1) S (x³ +1) Inx dx 2.) Sxe ²x dx 3.) S dy √y + 4√√y³ 73

A: We have to evaluate the given indefinite integrals.According to our guidelines we can solve only 3…

Q: Let fn, f be real functions on S2. Show ∞ ∞ ∞ {w: fn(w) + f(w)} = UNU {w: | fn(w) - f (w)| ≥ } }.…

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Q: for æ > 1. Using the Comparison Theorem, (a) determine whether the integral ro03+ g(x) Let 0<g(x) I2…

A: The solution of given problem is given as follows :

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A: 1) &gt; left sum will be greater than right because function is decreasing 2)  &lt; because…

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Q: 3, 5x 60(x 2 + x;), 3 b) Y = In 7.

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Q: Show that the identity k n = n 72 n k k-1, olds for all integers 1 <k<n and use it to prove that n…

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Q: (x- 1) (x– 2)(x+ 1) (x+ 2)(x- 3) (x+ 3) 2. Let f"(x) = and g'(x) = For what values of x are Az) and…

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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: The value (x, f(x)) of the maximum or minimum limit of the function 8 + f(x) = x3 - 6x2 + 4x and for…

A: Please see the attachment

Q: Prove or disprove (if false, give a counterexample): (a) If {n} and {yn} are both bounded above,…

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Q: (X-x) = 0 using summakion nules.

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Q: (b) A sequence (fn) of differentiable functions such that (fn ) converges uniformly but the…

A: To Explain: A sequence fn of differentiable functions such that fn' converges uniformly but the…

Q: f'(x) = (x+) (x-1) (x+ 7)(x-4)

A: We have givenf'(x) =(x+1)(x-1)(x+7)(x-4)A) critical points are at which f'(x) =0so,f'(x)…

Q: The following sum where b = and f(x) √√√√√»-()': - ( 5 )² · 5 + √/25 - (10) ².5 + ...- + n n is a…

A: Solution is below

Q: Use the Error Bound to find a value of N for which error (TN) ≤ 10. Let K₂ be the maximum of If"(x)]…

A: Given ∫257xdx, We have to calculate N by using error bound.

Q: Give an example of a function that is continuous on -∞ < x < o but is not differentiable at x = 3.

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Q: fn. (1,00) Evaluate lim

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Q: check if the fixed point itteration converge or diverge for  (6/x-5) in interval [4,5

A: f(x) = (6/x-5)

Q: check if the fixed point itteration converge or diverge for  (x^3/3)+4 in interval [4,5]

A: f(x) = (x^3/3)+4

Q: Find the length of the graph of f(x) = ² - In(x) for 1 < x < 10. 99 1 a) 4 -In(10) 99 + In(10) b) 4…

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Q: f(x) = x(x-1) for rational numbers          = 0 for irrational numbers  Prove f is continuous at x…

A: Given function is continuous at x= 0 and x=1. See the attachment.

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.