If x = t + 2 sin(at), y = 3t – cos(nt), evaluate at t =;

Q: What is y' of y = sin¹ (cos x)? O A. y' = ATHE sin + 1-cos² 1 O B. y' = 1 OC. y'= sin z 1-cos² z OD.…

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Q: Given t2 – 1 - f(x) = dt 1+ cos?(t) At what value of x does the local max of f(x) occur?

A: Given that      f(x) = ∫0x[(t2-1)/1+cos2(t)]dt  Here we have to find at which value of x does the…

Q: Given y= 5e3X + sin x, -is dx A) 5e3x + cosx B 5e3x – cosx 15e3x + cosx D 15е3х — сosx

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Q: FIND DY/DX OF THE FOLLOWING -y=sin' In (x+1)

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Q: Let z be defined implicitly as a function of x and y by the equation dz 4+ In (xy²) – cos (xy – 2) =…

A: Given: Let z be defined implicitly as a function of x and y by the…

Q: Determine the solution to this DE: Cosx dy +(y- cos"x)dn = 0 cos? x Idx = 0

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Q: If z = x?y + 3xy, where x = sin 2t and y = cos t, find dzidt when t = 0.

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Q: 2.) If H (y) = cos y – sin y, find H (0), H (n),H (T), and also show that H. n+ x) = H (n - x) = -H…

A: The solution is given as

Q: Solve for f(x) the ir f f(x) cos px 8 sin² t

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Q: Evaluate the definite integral. 1/2 cos(t) dt 75+ sin(t) 0.

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Q: The coefficient of Sin(x) in the antiderivative of F(x) =| cos is 17/16

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Q: z = y sin(2x) + (1 + x²)e* + cos x tan¬(y* + 1) In(y6 + 137)

A: ∂z∂x=∂∂xysin2x+1+x2ex+cosxtan-1y4+1lny6+137=∂∂xysin2x+∂∂x1+x2ex+∂∂xcosxtan-1y4+1lny6+137=2ycos2x+1+x…

Q: If f(x) = 5 sin x + 12 cos z, then %3D f'(x) = f'(2) =

A: The question has been solved in detail in the next step.

Q: Find an antiderivative F(x) of the function f(x) 10 sin x such that F(0) 1. 17+ cosx

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Q: Evaluate: Sv*+sin/x dx. A x+2cos/x+ C 2x+ cosx B + C 2

A: We have to solve the integral

Q: Given sin x + cos x = 1, find x for the interval 0 sx < 2n T/2

A: Find the value of x

Q: 2. If f"(x) = 4 sin x +16 cos x, f(0) = 6, f'(0) = 1, find f(x) and f ().

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Q: Find y' for the following 1- y5 + x²y3 + 18 = ye*² 2- Sin(x + y) = y² Cos x 3- 3x²-2y³-1=0, find at…

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Q: Use the Intermediate Value Theorem to show that the equation cos⁡x=e^x−2 has a solution in the…

A: Please rate and feel free to ask any query about any part of the question.

Q: If the function = (x)S x' +1 cos( 2 7x - a) if x < -1 is continuous at if x 2 - 1 x = -1 , find the…

A: Given: fx=cos2πx-aifx&lt;-1……1x3+1ifx≥-1……2   To find: Value of a where fx is continuous at x=-1.

Q: The result of dy/dx for the following function is COS X y = 1+sin x

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Q: dy iven that x = e" cos 3t, y=e" sin3t, show that tan 3t + dx %3D 4

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Q: dx. (a) [ cosʻ x+4 sin x (i) Evaluate Using the substitution ttanx

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Q: (1 + cos 7t) 2 sin 7t dt

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Q: Given that: z = y sin(2x) + (1+x²)e* + cos x tan¬1(y* + 1) In(y6 + 137)

A: z=ysin2x+1+x2ex+cosxtan-1y4+1lny6+137 Differentiating wrt x, we have…

Q: Using the substitution t = tan(), the integral 2 dx sin(x) – 78 cos(x) can be written as dt 39 – t-…

A: To make substitution and re write the given Integral.

Q: Suppose A(t) = [ e^t 0 0 0 cos t sin t 0 −sin t cos t]…

A: Given: At=et000cos tsin t0-sin tcos t To Find: To show that At-1 exists and then to find it.

Q: Determine Yp using undetermined coefficients: 2. (D2-1) y = e-x (2 sin x + 4 cos x)

A: The solution of the problem is given in the next step.

Q: sin(iny)dy is equal to * y (A none of these cos(ny) + C y cos(Iny) + C (D) -cos(iny) + с cos((ny) +…

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Q: y = sin(Ax + B)

A: We will find the Differential equation as following.

Q: Let I = 3x*cos (x) dx. The approximation of / using the two- formula is:

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Q: Given f(x,y,z) = cos(4xy) + sin(2z). Find fy(1,2,0). Leave your answer correct to two decimal…

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Q: Evaluate in x cos x dx. .3 I COS" T

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Q: Given f(x,y) = ex cos y, Evaluate fy(0,2) Oe2 0 0 O cos 2 O-sin 2

A: The given function is: fx,y=excosy   As we know that; The common derivative; ddxcosx=-sinx And…

Q: Consider the functions h : R→R and g : R -R defined by h(x) = 72 (5 + arctan(sinh 4æ)), . g(x) = 144…

A: Using inverse trigonometric  function properties

Q: Given f(x,y) = eX cos y, Evaluate fy(2,0) O cos 2 O sin 2

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Q: Given that f(x, y) - cos(x²) + 6e* sin y . Find fxyxyx · %3D

A: fx, y=x61+6y-cosx2+6exsiny Partially differentiating with respect to x, we get…

Q: For sin y=- find the value of so that (y+y")= - 1 at 1 at x=0 Cos X-

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Q: If f(x) = (e'7 cos(x))' 18e +12 sin(r) f'(0) then %3D f(0)

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Q: What would be your of 'du' using the IBP (e^x) (sinx )dx * none of the above e^x cos X sin x sin x…

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Q: The f sin x cos x dx is not equal to {A} -cos 2x + C {B }sin'x + C {c}-cos'x + C {D} sin 2x + C

A: Given query is to find the incorrect option for the integral.

Q: (f) If w=4x² +4y² +z² ,x= p sinø cos0, y= psinøsin0 , z =pcosø, Əw find and ap

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Q: Given that: z = y sin(2x) + (1+x²)e* + cosx tan¬(y* + 1) In(y® + 137)

A: ∂z/∂x  is the partial differentiation of function z with respect to x, keeping other variables…

Q: Find the clerivative of Y. a) y = Sin3x t cos3 x %3D b) y = tan? (x³) c) y=4 sec (5x)

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Q: If f(x)=e^2x cos(3x), then f’(0) = ?

A: Derivative Question

Q: Using an appropriate substitution, f sin®(x)cos³(x)dx is equal to:

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Q: Determine the ABSOLUTE EXTREME values of the function y = cos x + sin x, over the interval 0<x < 2T

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