Express the following limit as a definite integral: lim 2

Q: Evaluate the limit using L 'Hospital's rule: lim x to 0 e^x -1/sin(12x)

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Q: Determine the following limits analytically.

A: Given: L=limx→-1x2+8-5-4xx3+1 For evaluating given limit, we substitute x=-1+h, h→0 So,…

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

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Q: Evaluate the limitlimx→0+x (ln(x))^2

A: To determine the value of the limit.

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

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Q: Approximate the given limit numerically and verify your answer graphically. Round your answer to…

A: Given limit, limx→0+xlnx+x2

Q: x²– y? lim (x, y)→(0, 0) x² + y?

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Q: Evaluate the following limits. 1 - cosh x 1. lim x+0+ ln(x² + 1)

A: Note:- Since you have asked multiple question As per our policy, we will solve the first question…

Q: Find the limits in Exercise

A: Limits are used to calculate the approaching value of the function at which the exact value of the…

Q: Evaluate the limit using a definite integral 2 lim n n 1+

A: Let x = i/n Hence, dx = 1/n when i = 1; x = 1/n; As n tends to infinity, 1/n tends to zero. Hence,…

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

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Q: Express the limit as a definite integral. [Hint: Consider f(x) = x*.] lim n- 00 dx

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Q: Evaluate the following limit. lim (1+ ax)*, for positive constants a and b b lim (1+ ax)* = (Type an…

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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 derivative.

A: Given expression

Q: Express the limit as a definite integral on the given interval. lim n - 00 cos(x}) Дх, [2л, 5л] Xi i…

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Q: x + 2x lim х—0 х2 — 2х

A: Given : limx→0x2+2xx2-2x

Q: Express the limit as a definite integral. lim xk Ax [-3, 2] 4-0 k 1

A: Given

Q: x sin y lim (х, у)— (0,0) |x+ |y

A: To find: Limit of the given

Q: Express the limit as a definite integral on the given interval. n X;* -Дх, [1, 9] lim (x;*)² + 4 n-…

A: limn→∞∑i=1nxi*xi*2+4∆x,    1, 9 Here, fx=xx2+4, a, b=1, 9

Q: Find the following limits. Do not apply L'Hospital's rule. ペ-4 lim +2 |x– 2| (i) (ii) sin (3t) lim

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

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Q: Determine the following limits analytically.

A: Given: The limit expression limx→π21-sin3xcos2x, To find: The value of given expression.

Q: 9. lim 15 1 + (i/n)6

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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: Use L'Hospital's rule to evaluate the limit sin(3t) dt lim X-0 x2 O O

A: We have, limx→0∫0xsin3tdtx2 On solving further the integral part, we get the result as…

Q: Express the limit as a definite integral on the given interval. lim -Ax, [1, 3] (x†)² + 2 i = 1 dx

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Q: Compute the limit as xà0 of f(x)=(sin(61x))/x, if possible.

A: To find:limx→ 0sin61xx

Q: Evaluate the limit using L'Hospital's rule: et – 1 lim x→0 sin(9x)

A: Limit is 1/9 Explanation is given below

Q: Estimate the value of the limit to at least 2 decimal places. a² + 16x + 63 lim

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Q: Use direct substitution to find lim tan 0. O v3 O 1 O limit does not exist

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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: Evaluate the following limit. (-) lim| costi- 5 sin j+-k 2

A: Given,            limt→πcosti-5sin-t2j+tπk

Q: Express the limit as a definite integral on the given interval. lim 21 (x)2 + 7 Ax, [1, 8] dx

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Q: 2r (1- lim

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Q: 2xy lim (x,y)→(0,0) x² + y²’

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Q: Use L’Hôpital’s Rule to evaluate the limit.

A: This is in (0/0) form. Therefore we will apply L'Hospital's Rule to find the limit.

Q: a)Express the limit as a definite integral. Σ (3c-5)Ax, xe[0,1] lim 2 b) and then evaluate it.

A: lim∆→0∑i=1n3c2i-5∆xi  x∈[0,1]∑ =∫∆xi=dx∫01(3x2-5)dxThis is definite integral

Q: Express the limit as a definite integral on the given interval. lim S 19(x/)³ – 8x;]Ax, [2, 5] 1

A: The definition of definite integral is, ∫abf(x) dx = limn→∞ ∑i=1n f(xi*)△x   in the interval a, b…

Q: Evaluate the following limits using L'Hopital's Rule when possible. a) lim,- (2) b) lim (1+ æ) +0+

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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: Find the limit as x approaches negative infinity of (xe1/x-x)

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Q: Evaluate the definite integral by the limit definition. L₁x³dx

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Q: express the limit as a definite integralon the given interval

A: Question: Answer:

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: Express the limit as a definite integral on the given interval. lim [9(x*)³ - 2x*JAx, [2, 9]

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Q: Find the following limit and show that either the limit exists or not lim (x,y)¬(0,0) xy sin 2 + y²)…

A: claim - to show either the limit exist or not  limx,y→0,0xysin1x2+y2 as we know, limit exist if…

Q: Find the limit for the following functions: x-sinx 1-lim, x-Vx² + 2x 2- lim,-o

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