f X1, Y1, are two positive unequal numbers and Xp = (Xn- 1+ Yn– 1) and Prove that the sequences (xn) and ( y,) are monotonic and they nverge to the same limit. y,= Vx -1 Yn-1 V n22.

Q: dt converges. There is no value of r such that (3t)-" 14.

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Q: Use the figure to find the limit a in the interval [a, 4] such that f (x) dx is smallest. f(x) + 2 3…

A: To solve the following problem

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Q: The sequence an =n-Vn +1vn+3 converges to the limit A)-3 B) -1 C) 1 D) +2 E) -2 F) 0

A: Given:

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Q: What is the limit of f(x) = 8 as x approaches n? (If an answer does not exist, enter DNE.

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Q: Find Limit of .... as n approaches infinity    an= ((-1)^n)/n^2 bn = e^n /5^(2n)) cn = ln(n)/n^5

A: Definition used -           limn→∞(a)n=0a&lt;1∞a&gt;1           We can use the L'hospital rule when…

Q: Express the limit as a definite in 7 lim 1 + (i/n)3 n→ 0 n i = 1 1 7n dx 8

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Q: Find sequences (xn) and (yn) so that xn - Yn 0 and yet does not converge to 1 Yn

A: By Bartleby policy I have to solve only first one as these are all unrelated problems.These are all…

Q: Express the limit as a definite integral. n 7 lim 8 1 + i = 1 n- o n dx

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Q: f(x) = x(3x-(9x2+2)1/2). Compute the limit of f(x) as x tends to positive infinity.

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Q: Let            fn(x) = nx/1 + nx2  (a) Find the pointwise limit of (fn) for all x ∈ (0,∞).

A: Given : fn(x)=nx1+nx2; To find the point wise limit of this function for given values of x: We have…

Q: 3. Find the constant k that will make f continuous on (-0o, 00). Sx – 4 , (kx2 – 24x + 46, x > 5 x<5…

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

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Q: f (х, у) %3D х4 + 4y2/x2 + 2y2 f function is defined as. Does f function have a limit at point…

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Q: Express the limit as a definite integral. 7 lim n- 0 n 3 1 + (i/n) i = 1 '1 7n dx 8.

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Q: The limit lim (x,y) →(-2,-5) exists and is equal to -20. Select one: O True O False 25x²-4y² 5x-2y

A: The objective of the question is determine the limit existing.

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: 3. Given the function y = [(x² +2x+ 1]/(x), (x0), find: (a) the limit of y as x approaches positive…

A: Given:  The function y=x2+2x+1x, x≠0 To Find:  a The limit of y as x approaches positive infinity.b…

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Q: The limit of f(x, y) as y → 0 along the path a x=y is 1. The limit of f(x, y) as y → 0 along the…

A: Given: fx,y be a function with the condition the limit of y→0 along the path x=y is 1 and the limit…

Q: (4) Find the values of a and b so that h(x) is continuous at = 4. Hint: Write down the limit…

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Q: Find the limit as k approaches infinity of 1 + 1 10k 10 1 2 e

A: Given, limk→∞1+110k10k    We have to find the value of the above limit.

Q: Find f'(a) using the limit definition for 1 f(x) = V6 – 5x -

A:

Q: Let x1 O and xn+1 x+1 2 Show that (x,n) converges and find its limit.

A: It is given that  x1=0 and xn+1=xn2+12. Let xn+1=ϕ(xn)=xn2+12 By fixed point iteration method…

Q: Find the value of ſ (2x – x³) dx by evaluating it as the limit of sums.

A:

Q: Q2: (a) By using " L' Hopital rules "; Find the limits of ::- (1) lim,-(n/2)-(tan x)cosx (2) lim,--0…

A: L'Hôpital's rule states that for functions fx and gx which are differentiable on an open interval I…

Q: . Apply the two path test to make sure the following limit exist or not at (0,0) xy f(x, y) x³ +…

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Q: True or false? If k &gt; 0, then all solutions of y' = −k(y − b) approach the same limit as t →∞.

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Q: 2лу + ar? + ay? lim ax² + ay² z,4)¬(0,0)

A: lim(x,y)→(a,b) f(x,y)=f(a,b)

Q: Find limit of a, of the series (–1)"+1 (, Inn-

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Q: If X1, Y1, are two positive unequal numbers and Xn = (xn- 1+ Yn – 1) and y, = Vx, – 1 Ya-1 V n 2 2.…

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Q: 2 If f is continuous on [0, 2] and f(x) dx = 5, find the value of | f(æ – 2) dæ.

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Q: 1. Let f(r) 5r?. %3D (a) Using the limit definition, find f'(3). (b) Find the equation of the line…

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Q: If fn : R → [0, 0) is a sequence of integrable functions, fn + f a.e. as n → 0, and S fn + 0. Prove…

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Q: Use the figure to find the limit b in the interval [0, 10] such that 9. f (x) dx is largest. f (x) 4…

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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: 2 2 If f is continuous on [0, 2] and / f(x) dx = 5, find the value of | f(x – 2) dæ.

A:

Q: Find the limit of f(x) = as x approaches co and as x approaches - oo. 4 -

A: Given,          fx=-4+2x4-6x

Q: 2. Find the (exact) values of a and b so that f is continuous at a = 2. 8r2 + 20x + 28 if x 2

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Q: The sequence a=n-vn+1Vn+3 converges to the limit A) -3 B) -1 C) 1 D) +2 E) -2 F) 0

A: For a series ; if it converges then . If  the limit ; then the series diverges.

Q: Find the limit as x approaches -1 for O-1/2 O 1/2 O-1 01 x+2 -1 x+1

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Q: Find the limit of (x3+x2)1/2sin(((2)1/2pi)/x) as x approaches 0

A: To find

Q: Find the limit as x approaches infinity of the function V2 – x2 h(x) х3 — х + 1

A: Given:  h(x)=2-x2x3-x+1h(x)=x2 2x2-1x31x3-1x2+1  (Taking highest power of x in the…

Q: -6x, z 7. f(x) = 1, 6x, Find the indicated one-sided limits of A and determine the continuity of fA…

A: Given data:     The given expression of the function is: .   The below figure shows the graph of the…

Q: 2x Sí“(2t-2)² dt (a) Find the limit (if exist): lim 1 2х-1

A: