Use L'Hospital's Rule to evaluate each of the following limits. sin2z+7z2±2z 4. z2 (z+1)2

Q: 6x dx D.

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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 = 1…

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Q: Evaluate the definite integral by the limit definition. (x² + 2) dx

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Q: 4. For each of the following improper integrals, note WHY it is improper, and then set up the…

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Q: Express the limit as a definite integral on the given interval. im. (4(x;") - 3x;JAx, [2, 7] i = 1 7…

A: By limit definition of a definite integral, limn→∞∑i=1nfxi*∆x=∫ab f(x)dx  where ∆x=b-an and…

Q: 4. For each of the following improper integrals, note WHY it is improper, and then set up the…

A: Given: a. ∫1∞ 1x3 dxb. ∫-∞4 3x+2 dx To write: Why the given integrals are improper and to set up the…

Q: Find the indicated Midpoint Rule approximation to the following integral. 13 |3x dx using n= 1, 2,…

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Q: Use the Midpoint Rule with n = 3 to approximate the integral 16 | (- 10x + 2x2) dx 10

A: In this question we will use basic of calculus i.e concept of midpoint rule to approximate the…

Q: By using trapezoidal rule, n=2, The integral = π/2 sin (x) dx 0.9444 O 0.9481 O 0.94809 O 0.9482 O…

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Q: Find a value for n to ensure that the absolute error in approximating the integral x cos x dx by the…

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Q: Find "(x2 + 3)dx using the definition of definite integral (i.e. using a limit of Riemann sums).

A: Solve the following integral

Q: Evaluate the following Improper Integral. Does the limit converge? Why or why not? 1 dx xIn x

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Q: 39. Use the definition of the integral to find the exact answer to x*dx , that is find lim f(x, )Ax.

A: We are asked to evaluate the integral using definition of integral

Q: Use Simpson's rule to approximate the following integrals: (using n = 8 subintervals a. cos x³ dx

A: # as per the guidelines we are entitled to solve one question at a time, please resubmit the other…

Q: Estimate the following integral using the trapezoidal rule with n=10. 5² = 1+x² dx

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Q: What is the integral of sin^5 x dx if the lower limit is O and the upper limit is T/2?

A: We have to find out

Q: Use the definition of the definite integral a sum to evaluate | (2 – 3r)² dxr. as a limit of

A: Given:           I=∫-112-3x2dx To Find I using definite integral as a limit of sum:

Q: Evaluate the definite Integral by the limit definition. (x2 + 4) dx

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

A: Given expression limn→∞∑i=1nxiln2+x2i∆x,0,2 We know that ∫abfxdx=limn→∞ fxi∆x......1Where, ∆x=b-an…

Q: In order to evaluate the integral expression / In( sin(x ))dv using simple substitution, dv =f(x)…

A: Integration

Q: 4. Use the comparison property to calculate if the following integral converge: sin? x dx. | 1+

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Q: Evaluate the definite integral by the limit definition.

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Q: 00 1 -dx x3 – 1 1 4

A: Use the definitions of improper integrals to write the improper integral in terms of limits.

Q: By using trapezoidal rule, n=2, The integral J = -π/2 ST O 0.9480 O 0.94809 O 0.9481 O 0.9444 O…

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Q: 10 x2 +9 dx 5

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Q: Use the appropriate limits to determine if the following improper integrals converge or diverge. If…

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Q: 2x Vez +2 dx

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Q: State whether the following integral converges or diverges: cos x/ √ (2 − sin x) dx  limit: (0 to π/…

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Q: Evaluate the definite integral by the limit definition. L (x² + 4) dx X 31

A: use the limit formula for integration

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(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: Evaluate the following integral arctan x dx

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Q: Q5. Apply the mean value theorem for integrals to evaluate e Lim -dx. 2 + CoS x

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Q: Express the limit as a definite integral on the given interval. lim x, In(2 + x?) Ax, [0, 3] n- 00 i…

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Q: Use the Midpoint Rule to approximate the integral 15 (-læ – 3a?)da with n=3.

A: Given,  ∫715(-1x-3x2)dx

Q: 4. Use the comparison property to calculate if the following integral converge: sin? x =dx.

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Q: Which of the following definite integrals represents the limit: 1+ z?A¤ lim n00 You may use the fact…

A: Given:-limn→∞ ∑i=0nxi1+(xi)3 ∆x    on the interval 2, 5integral as limit of sum∫abf(x)dx=limn→∞…

Q: By using trapezoidal rule, n=2, The integral J = 0.9444 0.9480 0.9481 O 0.9482 O 0.94809 π/2 0 sin…

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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: Evaluate the definite integral by the limit definition.

A: Given: ∫031-2x2dx

Q: Use the appropriate limits to determine if the following improper integrals converge or diverge. If…

A: since u have asked multiple question in one task so we will be answering only first question.

Q: Evaluate the integral as a number, o, or –∞ or enter DNE if there is no limit. sin(x) dx = -cos(t) +…

A: Given: To evaluate the integral: ∫0∞sin(x) dx   Formula used: ∫0∞f(x) dx=lima→∞∫0af(x) dx

Q: Given a decreasing concave up function f(x) on the interval [2, 5] with f(2)=10, f(5)=3, f'(2) =-4,…

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Q: Evaluate the definite integral by the limit definition. x dx

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Q: For each of the following improper integrals, note WHY it is improper, and then set up the limit(s)…

A: We have to discuss the given improper integration.

Q: Express the limit as a definite integral on the given interval. „m. 2 (3(x;)° – 6x;*]Ax, [2, 6] i =…

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Q: Express the limit as a definite integral on the giv cos Xi Ax, [3x, 4x] lim Xi i = 1 4л dx

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Q: Evaluate the following improper integral: dx.

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