Find Limit of .... as n approaches infinity    an= ((-1)^n)/n^2 bn = e^n /5^(2n)) cn = ln(n)/n^5

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: Evaluate the integral if it converges and enter the exact value. If the integral diverges, indicate…

A: The given integral is ∫-1216x-13dx. We also know that ∫xndx=xn+1n+1.

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: 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: 8. Informally explain how the length of a curve defined by a function be computed with an integral.

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Q: Choose True if the statement is correct, otherwise False. One cannot determine the definite…

A: Choose True if the statement is correct, otherwise False. One cannot determine the definite integral…

Q: How are the derivative and the integral of a series of powers defined?

A: Consider the following power series with a radius of convergence R > 0. Let

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: Estimate (2x – 5) dx using right endpoints for n = 3 approximating rectangles. (2x – 5) dx is…

A: We have to estimate the , ∫15(2x-5)dx using right end points for n=3

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: prove that \int_3^(\infty ) e^(-3x)dx  converges to (1)/(3e^(9))

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Q: Evaluate the integral if it converges and enter the exact value. If the integral diverges, indicate…

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Q: Determine whether the improper integral diverges or converges. Evaluate the integral if it…

A: Given definite integral is ∫0elnx2dx.

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: ou have an opportunity to buy a business that will earn $10,000 per year continuously over the next…

A: To find: The present value of the business. Given information: A business that will earn $10,000 per…

Q: •4 x dx 10 x2 – 9

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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: Determine whether the improper integral diverges or converges. Evaluate the integral if it…

A: The given integral is ∫05125-x2dx. Check the convergence as follows.

Q: 1 dx if it converges. You may calculate the limit Calculate 3x + 9 by appealing to the dominance of…

A: Given:           ∫1∞13x+9dx

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: Evaluate the integral if it converges and enter the exact value. If the integral diverges, indicate…

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Q: Find the value of integral that converges.

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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: CK Show whye* dx does or does not converge.

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Q: find integal x over square root 4+x dx by any method.

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Q: In x dx 5.

A: Our Aim is to ∫ln (x)xdx -(i)

Q: Use Simpson's Rule with n = 4 steps to estimate the integral. 3 3

A: To estimate the integral ∫025x2dx with n=4. Formula used: ∫abfxdx ≈Δ…

Q: 4) 2²e*dx (Improper Int.)

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Q: Evaluate the integral if it converges and enter the exact value. If the integral diverges, indicate…

A: Let I is the value of given Integral.

Q: solve the integral: I2=  integral limit from 0 to 4= 1/((x+1) squar root of 2x+1) dx

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Q: -x² xe* dx -00

A: Given: ∫-∞∞xe-x2dx

Q: Determine whether the integral is convergent or divergent. -x2 3xe dx convergent divergent If it is…

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Q: Compute.  integral ln2x/x dx

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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: Šolve. In(-x + 1) – In(3x + 5) = ln(-6x + 1)

A: To solveln-x+1-ln3x+5=ln-6x+1

Q: The indefinite integral is often called the O antiderivative. constant of integration. derivative. O…

A: Please check step 2 for the solution.!

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: se limit methods to determine which of the two given functions grows faster, or state that they have…

A: Let f(x) = ex2 , g(x) = e10xIf limx→∞f(x)g(x)=∞ , then f(x) grows faster than g(x)If…

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: 19. Show that et grows faster as x→∞ than x" for any positive inte- ger n, even '.000,000. (Hint:…

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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: Use tangent line approximation to estimate 2390 (to seven decimal places), recognizing that 7* =…

A: To solve the following approximation

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 (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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Q: In the indefinite Integral in(cosh x + ex)- A sinh x + ex In(cosh x + sinh x tex cosh x + ex In(cosh…

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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.