81. The formula x" dx = limit of the general case by applying L'Hôpital's Rule to the limit on the left: +C is valid for n + -1. Show that the exceptional case n = -1 is a %3D n +1 lim t" dt = (for fixed x > 0) Note that the integral on the left is equal to n+1

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 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: 1. Use the definition of the definite integral as the limit of a Riemann sum to evaluate - 4)² dx.

A: “Since you have asked multiple questions, we will solve the first question for you. If you want any…

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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

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Q: 1. Write the improper integral which is represented by the following limit. lim C2" 2x dx x2-4 2.…

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Q: n, ]x| fn (x) = - 2m 0, x > 2n | fn (x) cos x dx lim Calculate its limit. What happens if the limit…

A: Write the integral as limn→∞∫-11fnxcosx dx=limn→∞∫-1-12nfnxcosx dx+∫-12n12nfnxcosx dx+∫12n1fnxcosx…

Q: Calculate  lim as n approaches infinity of the integral from 0 to 1 of (ncosx)/(n+ex) dx. Justify…

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Q: what is the value of a, such that the given limit is evaluated after applying L'Hopital rule twice…

A: We apply d'hopital rule when we get 0/0 form

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. in lim [5(x,")3 – 2x,*]Ax, [2, 7] i…

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Q: Express the limit as a definite integral. n 7 lim 2 3x Ax: [2,7] Ax,0 k= 1 O A. 3x' dx 2 о в. 3x'd…

A: We have to express the given series as a definite integral.

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. [4(x;")3 – 4x;1Ax, [2, 7] lim i = 1…

A: Solve the following

Q: Express the limit as a definite integral on the given interval. n eši -Ax 4 + X; lim [0, 2] i = 1

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Q: The area above the x-axis, below the graph of f(x) = between x=0 and x=2 is the limit of 1+z which…

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Q: Evaluate the integral. S tan (2x) sec (2x) dx .5 Find the limit

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Q: 23) Find the limit for the following function by using L'Hopital's Rule: x². e* lim x→0 tan² x

A: limx→0x2extan2x

Q: Express the limit as a definite integral on the given interva lim [2(xf)³ – 5x¡]Ax, [2, 5] n- 00 i =…

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

A: Definition of definite integral: ∫abf(x)dx=limn→∞∑i=1nfxi*∆x in the interval [a, b].

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

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Q: Do the followinç as indicated: 1. Use the definitic n of definite integral as a limit of Reimann sum…

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Q: Only one of these calculations is correct to evaluate the definite integral Inx dx Select one: Inx…

A: Integral test:  Integrals convergent if the associated limit exists and is a finite number (i.e.…

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

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Q: Use the Simpson's Rule with four strips to estimate the value of: L(-x In x)dx. Note that lim,0 x In…

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Q: so xe x dx

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

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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. cos(x) Дх, [2л, Зл] X; lim Зл dx 27

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

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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: 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: Calculate the integral 2 In(x) dx, if it converges. You may calculate the limit by appealing to the…

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Q: 4. (a) Explain why the integral (1+ x)3 dx is an improper integral. Determine whether the improper…

A: We have to find out

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: 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. cos(x;) lim n-0 i = 1 Дх, [2л, 5л]…

A: Given limn→∞∑i=1ncos(xi)xi∆xi in the interval [2π,5π]We need to express the limit as a  definite…

Q: Express the limit as a definite integral on the given interval. lim x; In(2 + x²') Ax, [0, 2] i = 1…

A: Given, limn→∞∑i=1nxi ln2+xi2∆x And interval 0, 2

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].

Q: Express the limit as a definite integral on the given interval. lim 8x; + (x;)² Ax, [3, 8] dx

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: 2. Determine if the integral converges or diverges. Part of your grade on this problem depends on…

A: Topic:- integration

Q: Express the limit as a definite integral on the given interval. lim (4(x")3 – 3x;]Ax, [2, 6] n- 00 i…

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Q: Express the limit as a definite integral on the given interval. lim [9(x,")³ – 4x†]Ax, [2, 6] n- 00…

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