12. Evaluate the limit ,kT. lim -> sin(-) n→∞ N n k=1 by expressing it as an integral.

Q: Evaluate the following by limit of su (3x² +5)åx (sin x)dx

A: Solution:To find the integration Formula:∫xndx=xn+1n+1+Csin2x=1-cos 2x2∫cos ax=sin axa+C

Q: Express the limit as a definite integral on the giveninterval.

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Q: Express the following limit as a DEFINITE INTEGRAL: lim k= lim =? k=1 n

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Q: Let n be a positive integer. For which n are the two infinite one-sided limits limx→0±1/xn^n equal?

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Q: Compute each of the following limits, or show that the limit does not exist. (a) lim (xyz + In(-x) –…

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

Q: Use l’Hôpital’s rule to find the limits

A: Given Data The limit is limy→0 √(ay+a²)-a/y.   Evaluate the given limits by using l’Hospital rule,…

Q: Determine a region whose area is equal to the given limit. lim 3i 1 + n- co

A: Note: Suppose f(x) is continuous on the interval a,b then ∫abfx dx=limn→∞∑ i=1nfxi∆x where ∆x=b-an…

Q: 7. Express the limit as a definite integral on the given interval: n lim n- 00 3 tan x; Ax , [0, 1 ]…

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Q: Express the limit as a definite integral on the given interval. in lim [5(x,")3 – 2x,*]Ax, [2, 7] i…

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Q: Express the limit lim E (3(x;)° – 5(x; )*)A¤; over [2, 6] as an integral. i=1 Provide a, b and f(x)…

A: Given the Riemann sum,

Q: 3. Prove the following using the epsilon-delta definition of a limit. 1 c. lim = 0 X→+o x-

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Q: Express the limit as a definite integral on the giveninterval.

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Q: 2) Use the definition of the definite integral to write 2 e* dx as a limit. Do not evaluate this…

A: In this we use the limit  definition of definite integral

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

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Q: express the limit as an integral (or multiple of an integral) and evaluate.

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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: Express the limit as a definite integral. 4 lim non + (i/n)- (i/n)9

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

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Q: to evaluate the limit. 3 1 v 78. lim x→ x Jo im In(1 + e') di | In(1 + e') dt 2

A: Answer is  1/2 Explanation is given below

Q: 2. Calculate the following limits. Justify your answer. L'Hopital's rule Rule ) (without using 2x +1…

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Q: Express the limit as a definite integral. n 8 lim 2 cAxK, where P is a partition of [6,14] ||P||→0…

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Q: 3. Express the limit as integral: n lim Σcos (27xt Ar 2(2πχ* ) over [0,1]

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Q: Express the limit as a definite integral. lim E cAx, where P is a partition of [9,11] |P|-0 k = 1…

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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: Find the following limit by evaluating an appropriate definite integral over the interval [0, 1 lim…

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Q: Write the limit as a definite integral on the given interval, where ci is any point in the ith…

A: lim△→0 ∑i=1n3ci+10△xi & the interval is -1, 5. If f is integrable on an interval a, b, then…

Q: Express the limit as a definite integral. n lim > 2 cAx, where P is a partition of [3,8] n00ks1

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Q: Express the following limit as an integral. lim E(- sin (9(x; )* - x;)) ax over [2,4) Ax over [2, 4]…

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Q: Set up the Riemann sum to compute the area bounded by f(x) = 2x2 + 5x + 3 and the x-axis, between x…

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Q: Express the limit as a definite integral. 5 lim 2 cAxK, where P is a partition of [2,11] ||P|→0k=1

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Q: Express the following limit as an integral. -2(x;)* – 9 3x; + 7) lim Ax over [1, 3] n-00 Provide…

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Q: Express each limit as a definite integral: n lim n→∞, i=1 πί sin + (4 2n. 2 5k -1+ 5k lim 2 п k=1

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Q: Express the following limit as an integral. lim 1-00- TL i=1 (2 (27)¹ + 3) 8-91 Ar over [1,6]

A: Note : As  per our guidelines we are supposed to answer only one question if there are multiple…

Q: e lim エ→e | e 1.

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Q: Express the limit as a definite integral. [Hint: Consider f(x) = x2.] lim i = 1 n' xp 1.

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Q: 3. Convert the limit below into a definite integral and then evaluate it using FTC. 3\²3 1+ n)+2(1+…

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Q: e2z – 1 lim sin(x) ,2x I→0

A: We need to use L'Hopital rule to find the limit of given function at x=0

Q: Compute the limit 1 e¯nt lim dt. VE n-00

A: Given: limn→∞∫01e-nttdt

Q: Express the limit lim n- 00 I E (6(2;)* – 3(z;)*)Az, over (5, 6) as an integral. | i=1 Provide a, b…

A: The limit is given by limn→∞∑6xi*3-3xi*2∆xii=1n To evaluate: The values of a, b and fx when the…

Q: 1. Compute the following limits (without using L'Hopital rule): sin(ræ) Va +4 – 2 (a) lim (b) lim 0

A: Use limit to solve

Q: Which of the following correctly expresses the limit lim as a definite n00 n5 integral? 1 A. 1 В. dx…

A: Solution is given as below:

Q: 1. Prove the following using the € - 8 definition of limit. (c) lim ² = 2i. z→1+i

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Q: Express the following limit as a definite integral. 1 Σ 2-2 IPl-0 k=1 lim Ax, where P is a partition…

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Q: Express the limit lim (4 sin (2rx:) + 6)Ar; over [2, 3] as an integral. n- 00 i=1 Provide a, b and…

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Q: Express the limit as a definite integral. lim 3 Xk, where P is a partition of [2, 3] k=1.k

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Q: Express the limit as a definite integral on the given interval. lim x, In(2 + x^)Ax, [3, 4] n- 00

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Q: Express the following limit as a definite integral: where a = , b = and f(x) = lim 84x n n? = √²…

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Q: By using the de finitionof the limit, prove thal (D Lim x (x+1)=D0 e) Linx cos= o

A: Let f(x) be a function defined in the open interval a,b and let c be a point in the interval a,b…

Q: Express the limit as a definite integral. n lim 2 20 AxK, where P is a partition of [ - 6, 1] ||P|→0…

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Q: Express the limit lim > (5 sin(27x; ) + 8)Ax; over [1, 5] as an integral. n→ 00 i=1 Provide a, b and…

A: To find the solution