3 5 3 - (+)-(-) -- " n rb integral, that is provide a, b and f(x) in the expression Given Rn i=1 3 n express the limit as n → ∞ as a definite f(x) dx.

Q: Write the following limit as a definite integral on the interval [5, 11], where c; is any point in…

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Q: Prove that x² + ¹² +2111²2 = y 1112 where prime denotes differentiation w.r.t.s. 1 1+p¹² 4 p² o² + P

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Q: 14 Find the limite by using L'Hopital Rule: X-I ①Lim 3x²-x²-2 sin 5x X 3 ③Lim 1-2 Sinx

A: Step 1: L'Hôpital's Rule: States that if the limit is in the indeterminate form of like…

Q: Use mathematical induction to prove the following statement derivatives of the function f(x) = x¯¹…

A: We have to prove that the nth derivative of  where  is using mathematical induction

Q: Q1/ Discuss the continuity of : 1 x+ for x 2

A: Since, you have post multiple question. I am answering first one. Please post again for remaining…

Q: 14k 14 as a definite integral. 8 Express the limit lim Σ n→00k =1 9 + + 121

A: Known fact: Let f be a continuous function on a,b. Then ∫abfx dx=limn→∞ ∑i=1n fxi ∆x where ∆x=b-an…

Q: Suppose that f: R (0, ∞) and that f'(x) = f(x) ‡ 0. Prove that (f-¹)(x) = 1/x for x > 0.

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Q: 9. How should f(0,0) be defined so that f(x,y) - (x + y)² (X+s x² + y² is continuous at (0, 0)?

A: The given function is: fx,y=x+y2x2+y2 is continuous at 0,0 To define f0,0

Q: (2) ykbäi * .. Find the value of Limit Below Vx + 11 – 4 lim x→5 X - 5 3/4 O 2/3 O 7/5 O 1/8 O 7/3 O…

A: Given: limx→5x+11−4x−5

Q: 1 S(t – 4t) dt

A: Given that: The limit is limN→∞ ∑i =1N  iN2 - 4iN×iN .

Q: 1. Function f is continuous on (-00,00). Find constant k. f(x) [kx² + 2x x-kx if x ≥ 2 if x < 2

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Q: Which of the following is the widest domain of function? A) (0, ∞) B) R - {0} C) (-∞, 0) D)…

A: Given that             f(x) = √x Here we have to find the widest domain of this function.

Q: The value of c of fox) -x*-2 x", in the interval [-2,2) such that f'(c) -0 is .A -1 ,2 ,0 .B -1,1 .C…

A: We apply mean value theorem Answer c)-1,0,1

Q: ss the continuit 1 x+- for

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Q: Which of the following is a graph of a functionf that satisfies the following conditions: • f'(x) 0…

A: d2dx2fx &gt;0  on  -∞,-1  Thus, the minima lies in region x =  -∞,-1    Thus, only graphs C and D…

Q: Please explain the question clearly with all the options(a Let f = C(R) such that f is an…

A: This is a problem of Advanced Calculus.

Q: Show that f is continuous on (-0,00) sin x if x 4 V

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Q: The graph of f is shown in the figure. 6. 4 х 14 -4 -6+ 2-

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Q: 9 f:(-0,0) U (0, ∞) → (∞,0) U (0, ∞0). Where f(x) х Show that f(x) is continuous at x=3 with the…

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Q: 3) √³/₂2 5 - dx -2 2x-1

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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: 7 + Vx + x dx

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Q: Discuss the continuity of the following function: (2* (1– x), x 0 x = 0

A: Consider the given:

Q: Express as a definite integral the limit as x approaches infinite of 1/n[(1/n)^2 + (2/n)^2 +...+…

A: Step 1: