25. Let f(x) be a continuous function. Express + ()] lim п—оо as a definite integral.

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

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Q: Express the limit as a definite integral on the given interval. -дх, [1, 6] (x;)2 + 8 lim n- 00 i =…

A: Given limn→∞∑i=1nx*ix*i2+8Δx and 1,6 We have to express the given limit as a definite integral.…

Q: Express the limit as a definite integral on the given interval. lim > x; In(2 + x;2) Ax, [2, 5] n-…

A: The solution is given below

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. [9(x†)3 – 4xj]Ax, [2,9] lim n- 00 i…

A: Express the limit as a definite integral on the given interval.

Q: Express the limit as a definite integral on the given interval. lim 2x,* + (x;")² Ax, [4, 9] i = 1…

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Q: How many times must l'hôpital's rule be applied to evaluate ex - e-X – 2x lim X + 0 X- sinx

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Q: Express the limit as a definite integral on the given interval. n lim x; In(1 + x²) Ax, [0, 1] i = 1

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Q: Express the limit as a definite integral on the given interval. n lim x, In(2 + x,-) Ax, [0, 4] i =…

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Q: Express the limit as a definite integral on the given interval. lim (5(x)3 – 7x]Ax, [2, 6] n- 00 = 1…

A: Consider the given limit and interval. limn→∞ ∑i=1n5xi*3−7xi*Δx and interval=2,6 Now, go through the…

Q: If - 2x +1 ,when X#! and fcx)= 3 when x= 1 show that The function fex) Continuous at X - 1

A: The detailed solution is as follows below:

Q: Express the limit as a definite integral on the given interval. lim X; V 4 + x3 Ax i = 1 [2, 3] n-…

A: Given the limit limn→∞∑i=1nxi4+xi3∆x in the interval [2,3]

Q: Express the limit lim ! as a definite integral. Evaluate the definite integral. nil+(:)

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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: Evaluate the definite integral: 6/x with the upper limit being 5 and lower limit 1

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Q: Express the limit as a definite integral.

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Q: Express the limit as a definite integral on the given interval. x lim n- 00 -Ax, [1, 6] (x/)2 + 6 dx

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Q: Express the limit as a definite integral on the given interval. [5(x;)3 - 3x;]Ax, [2, 6] n- 00 i = 1…

A: see below the answer

Q: Express the limit as a definite integral on the given interval. lim X; In(2 + x) Ax, [2, 5] i = 1 '5…

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Q: Express the limit as a definite integral on the given interval. n lim -Дх, [1, 3] (x*)2 + 8 i = 1 dx

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Q: Express the limit as a definite integral on the given interval. -Дх, +7 [1, 6] lim dx J1

A: The following limit is expressed in the definite integral as shown below

Q: 16. Show that f(x) = Vx - 2 is continuous at x=2 but not differentiable at x=2.

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Q: Express the limit as a definite integral on the given interval. n *2 lim 2x;* + (x;") Ax, [1, 6] i =…

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Q: Express the limit as a definite integral on the given interval. lim n- 00 [4(x;)³ – 4x;"]ax, [(2, 7]…

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Q: Express the limit as a definite integral on the given interval. lim Ax, [1, 4] (x;)2 + 3 dx Need…

A: Given query is to write the expression as integral.

Q: Evaluate the definite integral by the limit definition. 3x2 dx

A: Please refer the attached image for complete solution. THANK YOU.

Q: Express the limit as a definite integral on the given interval. lim Ax [О, 6] 9 + X; i = 1 dx

A: The answer is found in step-2

Q: Express the limit as a definite integral on the given interval. lim x; In(1 + x?) Ax, [0, 1] dx

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

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Q: cosx * sin? (3x) 2 2. lim x→0 x2

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Q: Express the limit as a definite integral on the given interval. cos(x;) Дх, [Зл, 4л] Xi lim i = 1 4л…

A: By definition of definite integral as limit of sums is

Q: Express the limit as a definite integral on the given interval. x, In(2 + x) Ax, [0, 2] lim dx

A: I am going to solve the given problem by using some simple calculus to get the required result.

Q: Express the limit as a definite integral on t lim n-oLX; In(1 + x;²) Ax, i=1

A: Given that: 1. limn→∞∑i=1nxiln(1+xi2)∆x, [0, 1]2. ∫13(x-4lnx)dx

Q: Express the limit as a definite integral on the given interval. -Дх, [1, 8] lim х? (x;)? + 8 Ax dx

A:

Q: Express the limit as a definite integral on the given interval. lim Σ Σ x;* -ΔΧ, [1,4] 0-700 (x;*)2…

A: To express the given limit as a definite integral.

Q: Express the limit as a definite integral on the given interval. n x;* lim -ΔΧ, [1, 7] n→∞ dx i=1…

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Q: Express the limit as a definite integral on the given interval.

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Q: 1. Use the definition of the definite integral as the limit of a sum to evaluate (4.x – 2²) dx.

A: The given problem can be solved as-

Q: Express the limit as a definite integral on the given interval. exi Ax 3 + x; lim [0, 4] dx

A: We need convert summation in to integral

Q: Express the limit as a definite integral on the given interval. n exi lim -Ax [0, 9] n→∞ i = 1 6 +…

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Q: Express the limit as a definite integral on the given interval. * n Χρισ lim Σ -ΔΧ, [1, 8] 0-00…

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Q: In n n=2

A: The given expression is, ∑n=2∞lnnn The integral test says that for a series ∑n=2∞lnnn converges if,…

Q: 4. Determine if 1 1 sec if – 1 1 x – 1 is continuous or not at x = 0 and 1. In the case of…

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Q: Show that the function xsin f(x)%D 0, When x 0 is continuous but not differenti able at x = 0 When x…

A: Let f be a function defined in the neighbourhood of 'a'. Then the function f is said to be…

Q: Express the limit as a definite integral on the given interval. lim -Ax, [1, 6] (x)2 + 5 n- 00 dx…

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Q: Use the definition of the definite integral as a limit of a sum to evaluate (x² – 4x - 2) dx -2

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Q: Express the limit as a definite integral on the given interval. 5 V 3x; + (x;) Ax, [2, 3] * lim n →…

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Q: Express the limit as a definite integral on the given interv * 2x, + (x;")² Ax, [4, 8] lim n- 00 i =…

A: Given that: limn→∞∑i=1n2xi*+(xi*)2∆x,   [4, 8]

Q: Express the limit as a definite integral on the given interval. lim 2 x;)?+9 -ах, [1,4] (x;")² + 9'…

A: Use;∫abf(x) dx =limn→∞ ∑n=1n f(xi) ∆x                       over the given interval [a, b].