Given that f"(x) = cos(x), f'(T/2) = 2 and f(T/2) = 12 find: %3D - f'(x) = f(x) =

Q: findthe differential dy of the given function. y= arctan(x − 2)

A: we have to find the differential dy of the given function. y= arctan(x − 2)

Q: dx (2) S V9-x² E(Ctrl) X. 2x sin-1(구)+ sin-1 (민 + Option 1 Option 2 2x cos-1(민 + c CoS Option 3

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Q: if f(x)=2x-cos(x), Use Newton's method to approximate x, starting from the initial value xo=0

A: Solution:-    fX=2x-cosX           x0=0    f'x=2+sinxwe know      x1=x0-fx0f'x0           =0-f0f'0…

Q: find a particular solution yp of the given equation. primes denote derivatives with respect to x.…

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Q: Find dy/dx by implicit differentiation. y cos(x) = 5x² + 3y2

A: In implicit differentiation, we differentiate each side of an equation with two variables by…

Q: Can you help me step by step?

A: The given function is,

Q: arctan x Xe fel Xaresecx d

A: Since you have posted a question with multiple sub-parts, we will solve first three sub-parts for…

Q: Evaluate / x cos(128x)dx. Use capital C for your constant of integration.

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Q: Find dy/dx of y = cos^-1(2x) * sin^-1(2x)

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Q: If N(x) = sin x – sin θ and D(x) = x – θ, find the limit of N(x)/D(x) as x approaches θ. (SOLVE BY…

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Q: 23 Find dy/dx on the graph y3 sec/x2 + y2 = cos2x at point (1, 2).

A: Use product and chain ruleof differentiation at given value

Q: Let z= sin (y2 – 4x), Find the rate of change of z with respect to y at the point (2, 1) with x held…

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Q: Find the 4th order differential of the function y=√2x+1.

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Q: Since dv = cos( cos9 x) dx, integrate the differential equation to obtain the function v. V = ^p -…

A: We have to find solution

Q: 4. Integrate COs x dx

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Q: A particle, initially at rest, moves along the x-axis such that its acceleration at time t > 0 is…

A: Given a(t)=cos t Integrating with respect to t to get velocity function, vt=∫atdtvt=∫cos t…

Q: Find dy/dx for y = 3[(sin-(e-3x*))2

A: Given,          y=3sin-1e-3x22

Q: in integrating the function fx cos() dx using intogration by parts, whut would you choose for your…

A: Solution

Q: (b) by using gamma function x-1/3e-Bx dx

A: Gamma function

Q: 1. S e sin 4x cos 4x dx 2. S dx Je-2x dx e 2x

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Q: Find dy/dx if y= cos-1 In(x+1)

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Q: Let z= sin (y²– 4x). Find the rate of change of z with respect to x at the point (2, 1) with y held…

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Q: Integrate: x² cos(2x) dx

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Q: Ssin (2x)cos(2r)dx

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Q: The position of a particle moving along the x-axis is x(t)  = sin(2t) - cos(3t) for time t>= 0. When…

A: Given the position function, x(t)=sin2t-cos3t

Q: Find dy/dx by implicit differentiation. 3 cos (9r) sin (2y) = 8 dy/dx =

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Q: A particle, initially at rest, moves along the x-axis such that its acceleration at time t > 0 is…

A: Given acceleration, a(t)=cost,       t>0 And v(0)=0, x(0)=3

Q: find dy / dx by implicit differentiation.

A: Implicit differentiation is performed when the dependent variable cannot be explicitly written as a…

Q: Cos 5x dx 3 +Sin 5x 1. 2. dx J16-9 (n x)²

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Q: ey sin x = x + xY %3D

A: Solution:- The given implicit function is  ey sinx=x+xy

Q: 11. Find dy/dx of In(x² + y²) + 2 arctan

A: Since the student has posted multiple questions and does not mention any specific question, so we…

Q: If y = sin2x, the derivative dy/dx is equal to a. cos2x  b. sin2x c, 2cosx  d. 2sinx (SOLVE BY…

A: Solving the equation by the method of differentiation.

Q: (a) Determine f 2xe3*dx by using integration by parts. (b) Determine S cos(x²) 2x dx by using…

A: Given,  ∫2xe3xdx ; We have to integrate using integration by parts ∫cosx22xdx ; We have to…

Q: In integrating the function fx cos(3x) dx using integration by parts, what would be your v?

A: Solution

Q: In integrating the function fx cos(3x) dx using integration by parts, what would you choose for your…

A: Let ,I=∫ xcos3xdxSubstitute  u=3xdifferentiate du=3dx⇒du3=dxI=∫ u3cosudu3I=∫ucosu9duTake the…

Q: In integrating the function f(3x + 5)(cos ) dx using integration by parts, what would be your du?

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Q: Find dy/dx by implicit differentiation. y cos(x) = 5x2 + 2y2

A: We can find the derivative using implicit differentiation as below.

Q: S" cos de 4. 2 dx .2 -1 1+x² 5.

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Q: valuate f¹² Vsin x + 1 cos x dx.

A: Topic:- application of integration

Q: 1- Find the equation of the tangent to the 2(x2 + y2)2 25(x2 - y?) at (3,1) 2- Find dy/dx for y =…

A: (1) given equation is                                              2x2+y22=25x2-y2,   at (3, 1)…

Q: Find dx (e3t + 1)dt. -cos(3rx)

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Q: Find dy/dx by implicit differentiation. sin x + 2 cos 2y = 1

A: the given implicit function is: sinx+2cos2y=1 we have to find dydx by implicit differentiation

Q: The Bernoulli's equation dy +ytanx = y'sec x after multiplying dx -2y and use appropriate…

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Q: dy/dx of y=5^cos(3x+5)

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Q: 1. Given dx [arccot u] = find the first derivative with respect to x of arccot v2x + 2. 1+u?

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Q: of y = In || dx 4 1-cos x 1. 1+cos x Find the

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Q: (a) f* (1 – cos 3t) sin 3t dt,

A: Since you have asked multiple questions in single request.so we will answering only first question.

Q: Find dy/dx by implicit differentiation. y cos(x) = 4x2 + 5y2

A: To find dy/dx by implicit differentiation,  given y cos x = 4x2+5y2

Q: B4. Evaluate e* sin x dx by using integration by parts method.

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Q: A-The derivative is y = In Vsin 0 cos 0 1 + 2 ln 0

A: Let's find derivative of given  function.