The improper integral f(x)dx can be written as lim f(x)dx + lim_ f" f(x)dx . w--00 w+00 If f(x) = 4e-3* , which of the following conditions is correct that makes the improper integral diverges ?

Q: Express the limit as a definite integral on the given interval. cos(x¡) Дх, [Зл, бл] Xi lim бл dx…

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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 =…

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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: Use L' Hopital's Rule to find the limit as x approaches positive Inifinity of:  ln(x)-ln(1+x) Hint…

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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…

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Q: Illustrate the setting up limits of a double integral?

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Q: Express dx as a limit of left Riemann sums but do not attempt to eval- x2 uate the limit.

A: Given, ∫-11-6 5x2dx

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: What is the limit as x approaches 0 of 2x/sin(2x)? Do so without using L'Hopital's Rule.

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Q: Evaluate the definite integral by the limit definition

A: Here,

Q: Express the limit as an integral. * lim (5(x)2 - 2(x;)³)Ax over [0, 3] i = 1 dx

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Q: Find the limits by using L.Hopital rule : 7x 1. lim x-0 sin 2x x2-16 2. lim x4 (Vx+5)-3

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Q: If the integral diverges, indicate that using the checkbox. 6 dx The integral diverges x(x + 1)

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Q: 2. Use L'Hopital's rule to find the limit; * - sin (*)= lim メ.Sin メーラ0

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Q: V5+s-V5 lim s→0 S

A: lims→ 05+s-5s=lims→ 01s+5+5Plug in the value s=0=10+5+5=125

Q: Compute the derivative of h(x) = 3x – 5 using the limit definition (do not use L'hopital's rule).

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Q: Find the integral.

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Q: Use integration by parts to prove the reductionformula.

A: Consider the following integration by parts formula: ∫uvdx=u∫vdx-∫dudx∫vdxdx ILATE Rule: We have two…

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Q: Only one of these calculations is correct to evaluate the definite integral Inx dx Select one: 1 Inx…

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Q: Express the limit as a definite integral on the given interval. lim (2-5(x,)² + 6(x;")³] Ax, [0, 4]…

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Q: Estimate the limit numerically or state that the limit doesn't exist: sec-{z) lim z¬1+ vz²-1 (Enter…

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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: Approximate the integral from upper limit 1.5 to lower limit 1 x^2 ln xdx using Gaussian quadrature…

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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…

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

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

Q: Explain why the improper integral (x + 3) sin(x) dx L. (x² + 1)(x² + 4)² is convergent. 8

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Q: -x² xe* dx -00

A: Given: ∫-∞∞xe-x2dx

Q: Use the definition of definite integral (as the limit of a sum) to evaluate | (2x – 1)° dzr.

A: ∫-212x-12 dx Here, a=-2,  b=1  &  fx=2x-12 Now, ∆x=b-an=1--2n=3n

Q: 2+x2 lim X→0 X-2

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A: Let u=tan(x). then x=tan-1u and  dx=tan-1u'du=duu2+1

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

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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: Evaluate the improper integral if it is convergent. (If it is divergent, type DIVERGENT.) 8e -x/2 dx

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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: Express the limit as a definite integral on the given interval. cos Xi lim Ax, [3π, 5π] 818 5m 3m dx

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Q: Express the limit as a definite integral on the given interval. cos X Дх, [Зя, бя] lim 6x X dx 3x

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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: How would I find the limit of the attached equation using L'hopitals Rule?

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Q: What is the limit as x approaches 0 of 2x/sin(x)

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Q: Use integration by parts to evaluate the definite integral: ∫3se^-4s ds with an upper limit of -0.9…

A: A=3∫abse-4sds , solving A where a,b are upper and lower limits as per questionIntegrate by parts…

Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.