Verify S Tokes' Theorem To 2.

Q: Use the Fundamental Theorem of Calculus, Part I, to evaluate d de -dt

A: We have to find

Q: OLet @ = (0,1)n Q = {x€ @104 x<1}. Prove that %3D 2) 2000m

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Q: Use the fundamental theorem of calculus part 2 to evaluate the 16 integral: S 3/rd 9 Note: Convert…

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Q: Evaluate the integral, 12 sec(4t) dt 2+3 tan (4t) dt = 2+3 tan (4t)

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Q: Prove fulay's formule -CstD)4isin LO)

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Q: Prove Taylor's theorem.

A: The objective is to prove Taylor's theorem. According to Taylor's theorem we have, If fx be a…

Q: 11. S 8a'da = %3D

A: This is a problem related to integration. Based on the general formula of integration we will solve…

Q: dr 1. Find if dt

A: Follow the procedure given below.

Q: 3dz 1. S 4-5z

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Q: Prove thiat dx Ś (areten()) ) = し 4+X

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Q: A. Homo ge neous Higher Ordered DE (0-704 - 310° ° + 103o² 1030² + 1500 - 216) y:0

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Q: Evaluate the integral. "T/3 8 sec 0 tan 8 de IT/4

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Q: What is Taylor's Theorem?

A: Taylor's theorem gives an approximation of a K-times differentiable function around a given point by…

Q: 2² + e4 z lim z 0 22 – e²

A: This is a form of infinity by infinity so we have to apply Lhospital rule that is differentiate both…

Q: 4. Compute f'dr by using fundamental theorem of integral calculus.

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Q: evaluate the definite integral.

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Q: Use the fundamental theorem of calculus part 2 to evaluate the integral: 2 dr Note: Round to the…

A: Evaluate the integral using Fundamental Theorem of Calculus Part 2 : ∫169xdx

Q: Prove that Cosh [m(t-x) Cosh mh 2mL 2mL

A: The given data is: To prove: emx1+e2mL+e-mx1+e-2mL=coshmL-xcoshmL

Q: Evaluate the integral 9t tan (1) dt

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Q: Anti der ivent ive 2x %3D 37-4

A: Solution

Q: Find dy ax 9=бл+бай

A: Given :y=x+1+xformula : ddxx=12x

Q: Inn NTT <os 2. n=1

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Q: Using the substitution u = 2x – 1, prove that - -3 8 dx 1 (2x-1)3 25

A: The given integral is ∫13x(2x-1)3dx Put 2x-1=t⇒2dx=dt when x=1 then t=1 and when x=3 then t=5 So,…

Q: (Superman Versus m ers arrive according uho

A: System 1 Customer arrival rate in a Poisson Process λ Service time  3μ System Capacity…

Q: az Find for z = x'y'eV

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Q: 6) Prove mathematically that (1 grad = 0.9 deg) %3D

A: Since, this is a multiple question according to the Bartleby Answering rule, only first question is…

Q: Prove using the IVT. ex + In x = 0 has a solution.

A: IVT: If f is continuous on the closed interval [a, b], f(a) ≠ f(b) and k is any number between f(a)…

Q: Differentiate the following with respect to x: b) 3*Inx

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Q: 11. Prove that tanh y du = In cosh u + C

A: The integration of the integral is tanhu.

Q: Find the indefinite integral 9t dt 9t dt =

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Q: (14) Approximate S, x² ex², Using Simpson's rule dp,

A: Simpson's rule is a numerical method used to approximate the definite integral which represents the…

Q: Fincd dy for y-sinner} er tot

A: Explanation of the solution is given below...

Q: So So t² etu du dt

A: Given, ∫03∫0tt2etududt

Q: to itself. Show all your work to recei

A: given as,

Q: it is unbaised estimated of a Then Show That ta is baised estimated of 02. Theorem:- if

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Q: Briefly discuss the origin/history of De Moivre's Theorem.

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Q: Proved that cosh fas/ (cashZ+L)

A: To prove :  cosh2z2 = 12cosh (z) + 1

Q: 27 Use the Fundamental Theorem of Calculus to evaluate S (Vx2 -) dx. 8.

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Q: Use Euler-Maclaurin's formula to prove that E n %3D

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Q: V1+ vz dz

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Q: 5 Evaluate ſ“ S" r² sin ø drdøde 0,

A: Evaluate: ∫02π∫0π∫05r2sinϕdrdϕdθ

Q: Find the lenegth of the cunde 312 2 from x=o to -

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Q: The term r ryis homogenous of degree two. -

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Q: Solve in terms f Bessel's functrom the folowrng (z=) DES?

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Q: Evaluate the improper intergal 1 -00 dx using the residue (x² + 16)3 theorem. 00 2

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Q: Evaluate the integral /_s 10+2z dz. 24 00 1,

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Q: Evaluate the integral 22 V4 – 22 dz 0.

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Q: e){x*,x%,x}on(0,)

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Q: Finl dy for

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