(e²)(sin²2x) Compute In y and In 5z

Q: 1 Show that L-1{ = (sin hat sin at) s4+4a4, 2a²

A: It is given that, L-1ss4+4a4=12a2sinhat sinat. A partial fraction decomposition of ss4+4a4:…

Q: 4. Show that sin(0 – ø) R2 – 2r R cos(0 – 4) + r² dø = 0. -

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Q: Find the critical numbers of f(0) = 2 cos 0 + sin² 0.

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Q: The approximation of 1 = cos (x² + 3) dx using simple Simpson's rule is: -1.57923 -0.93669 This…

A: The given integral is I=∫01cosx2+3dx To approximate the integral using Simpson's rule.

Q: V. Show that: 1. [(cosx-sin x)'dx = x+ cos 2x +C 2.

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Q: x³y"+xy'+4y = cos (2 In x)

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Q: 1 1 S [ sin(1+ y²)dydx= 1- cosl a. 2 cos 5

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Q: of cos 2 2 sin 0) de has the form 1 -F 4 sin lue of 0 to make F(0) =0?

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Q: 8F OF OF 1. Use the formulas above to find and ду ax exy + sin (xyz) + In (yz) = 4 – z

A: Partially differentiate the function with respect to x.…

Q: リ=!-Cos2x 1+(os 2x prove y = 2 tanx .secx

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Q: Q3. Show that дхду for дудх f = x² siny – 2y³ cos2x (

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Q: If y = √√1-x² sin¹¹x, prove that (1-x²)+xy=1-x². dx

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Q: .Find a reduction formula for ea* sin" x dx. Hence evaluate e* sin x dx. 3

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Q: 18 a Show that / (1 + sin 2zx)dx = n, for all positive integers n. b Sketch y = 1 + sin 27x, and…

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Q: 3 O f sin 2x cos 2xdx 4)

A: we use substitution method

Q: dt cos (2 sin 21) /1– 4r

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Q: The approximation of I cos (x²+5) dx using simple Simpson's rule is:

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Q: Find / sin(2r) PV -dr R I +4 by invoking Jordan's lemma.

A: Sol

Q: Evaluate 1 ei sin x cosx dx using Simpson rule with h = 20

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Q: Q1: Use the Improved Euler method to find y' = cos2x + sin3x ,0<x < 1,y(0) = 1, with h = 0.25. %3D…

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Q: y" + 2y' = sin 2x ||

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Q: Evaluate the integral. sin (3t + 17) dt cos (3t + 17) sin (3t + 17) dt = - 2, cos (3t + 17)

A: Consider the integral

Q: b) Is S cos4xv2 – sin4x dx = V(2 – sin4x)³ + C true or false? show me %3D

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Q: 7 Use the Intermediate Value Theorem and Rolle's Theorem to show that the equation 2 = sin z+1 has a…

A: use the intermediate value theorem and Roll's theorem to show that the eqautionx2=sinx+1has a…

Q: (2) If y = (sin-1(x))², prove that (1- x2)y" – xy' - 2 = 0.

A: here first we will derivative with respect to x then squaring both side and put value of the y then…

Q: 3. Solve the IVP: siny(x + siny)+2x²cosy y'=0; y(-1)= π/2 (Subst. first and then Bernoulli's)

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Q: Evaluate the integral. sin (8t + 16) dt cos (8t + 16) sin (8t + 16) dt = cos (8t + 16)

A: Solved below

Q: Find dy if y= 5x² sin4x dr O None -20x? cos4x – 10xsin4x 20x² cos4x + 10xsin4x O 10x² cos4x +…

A: We apply u*v rule of derivatives d/dx (u*v) = v*du/dx + u *dv/dx

Q: Find the general solution using reduction of order. 1. y''+y'=cos(4x)

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Q: Please I want solution of question 8 with step by step. Many Thanks

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Q: The integral S sine de 1+ cose sec²0 de 1+ tan cose de 1-sine sece tane de sece-1 S x dx x²+√√x²-1-1…

A: dsecθdθ= sec θ.tan θ

Q: Obtain the General Solution of: (z + 2)* cos yudz - [sin y In(3z 4 6) – d

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Q: Find the general solution of the differantial equation given by www |y" – 4y' + 5y = 3xe* – cos2x +…

A: Given y''-4y'+5y=3xex-cos2x+x+1sin2x

Q: (9) Verify that Yp = sin 2x is a solution of y"– y = -5 sin 2r and use it to find the general…

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Q: 2. Determine one real root of 8 (sin x) e¯* – 1 = 0 with xo = using three iterations of Newton-…

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Q: Compute L {sin(2t)e"}.

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Q: B\ Suppose that = 4 cos² t , x = d²y =- V3 sin(2t) and 0 <t <n. Show that sec3 (2t). dy 2 tan(2t)…

A: Dear student, there is a mistake in the question. The second derivative should be…

Q: 2. Evaluate the integral J cos (3x) sin°(3x)dx in two ways, one with u = u = cos(3x). Even though…

A: Given: Apply u-substitution method. Use two methods u=sin(3x)  and u=cos(3x)

Q: 2 2 sin (2t) dt. 8 - cos (2t)

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Q: 3 Q19- if z =- 4x³y sin sin (x³y) əz find əx

A: We want to find partial derivative of the given function.

Q: Evaluate the integral. sin (6t + 17) -dt CoS 2 (6t + 17) sin (6t + 17) dt%3D cos 2 (6t + 17)

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Q: Find [(1 - cos² t)dt]. dx A. sin²x B. -sin²x C. 1 - sin²x D. - cos²x

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Q: (4) find dy if 3って - ソ= e* (2Co83x +3Sin3x) e = Sin (x+3y).

A: Given 1. y=e2x2cos3x+3sin3x 2. e2x=sinx+3y

Q: e3x [7 sin 7x + 3 cos 7x] +C 58

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

Q: If we let u = 4x – 1 for theS 2 tan(4x-1)-3 cos² (4x-1) dx, what will be the resulting integrand?…

A: Solving the problem by finding the integrand.

Q: b) Is S cos4xV2 – sin4x dx (2 – sin4x)³ + C true or false? show me

A: this is false because

Q: The integral (cos(3x)) sin(3x)dx under the change of variable u = cos3xbecomes v uz du. -9/29 Select…

A: Given,