2. For the function f(x) : = sin x. Show with the aid of the elementary formula. 1 1 (1- cos 2A) sin? A = That f (x + y) – f (x) = = cos x sin y – 2 sin x sin?

Q: (a) Is Rolle's Theorem applies for the function ƒ(x) = cos(sin¬'x) on the closed interval [-1, 1]?…

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

Q: For a non-linear function, f(x) = cos(x) + 2 sin(x) + x², find the root using the following method:…

A: Given a function fx=cosx+2sinx+x2 To find the root of the function using secant method with x0=0,…

Q: 1. 6(x) = e- sin a, for y' + y cos x

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Q: Given f(0) = 7 cos 0 + sin 0. %3D a. Express f(0) in the form of R cos (0 – a) for R > 0 and 0° < a…

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Q: Suppose z is a function of x and y. Solve for ∂z/∂y if tan √(y^2 + x^2 + z) = z^(x)e^(6y).

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Q: Determine the exact x– value(s) of the intersection points of the functions f (x) = 4 sin² +7 sin 4…

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Q: 1 f(t) dt = ln(x) cos(x) + /. e* f(t) dt, find f(x). You may find FTC 1 useful. n(3) Given sin(3)

A: The solution are next step

Q: Use a CAS to plot the implicitly defined level surfaces in Exercises 73–76.

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Q: 4. Given f(x)= sin 6x cos 6x dx , what is f| | if f(0)= x ? A. π В. О С. 2л D. — я

A: This integration can be integrated by using substitution method. Clearly it is observable that put…

Q: Let  f(x) = cx + ln(cos(x)).  For what value of c is f'(pi/4)=4

A: sol:-    Given f(x) = (x+ln(cosx)  differentiating ω. r.t   x, we get    f1(x) = c+1cosx(-sin x)…

Q: Topic: Variable Separable and Homogenouse D.E. I need particular solution for 4

A: We have to solve

Q: I. Obtain the general solution of the following: D. (3D2 + 12)y = tan x E. (D2 − 3D + 2)y = cos…

A: We have to obtain  general  solution of given differential equation.

Q: h(x) = sin² x + cos x О<x< 2л

A: We have to find the functional value at where either function is not differentiable or derivative…

Q: 4.2 Given g(x) = ) = cos z + sin for 0 <<, find the value of f(x + 1)dg(x). END

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Q: 3- the solution for the following O.D.E y' = In(x) + tan (x) %3D

A: Since you have posted multiple questions i can do first question as per our company guidelines…

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: Given a function f(x,y,z) = (x+4) ln (9y - 2) sin (2z). Find the domain of the function.

A: Let's find.

Q: x sin y = y cos x +c

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Q: For the function f(x) = sin x , with the aid of elementary formula sin2A = 1/2 (1 − cos 2A), show…

A: Given that fx=sinxfx+y=sinx+yfx+y=sinx cosy+cosx siny by addition formulaNow ,       fx+y-fx…

Q: After applying variation of parameters to y " +y = sec(x), the following equations are obtained c{…

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Q: If f(t) = cos t and f(0) what is the exact value of 4 f(0) + f(0+ 27) + f(0 + 47) ?

A: Given : f(t) = cos t and f(θ) and -1/4

Q: In solving the antiderivative of f(x) =- 2- sin(x) by miscellaneous substitution, the substitution…

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Q: f (x) = xe-* – sin?x Newton Raphson (1st Method) @ x1 = 0.5 Newton Raphson (2nd Method)@ x1 = 0.5…

A: Newton Raphson Method:- Hence by Newton Raphson Method Root of the equation is 0.61447 (correct…

Q: 5. ) Using the Method of Undetermined Coefficients, give an appropriate guess for y,. y(4) + 9y" =…

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Q: Analyze the approximate value and the exact value for (7.2, 4.02) for the function z = x³y2 sin(xy)…

A: Below given clear explanation .Have a look in hand written solution below

Q: 2. Find (in terms of t): x = 2 + 3 sin t y = -1+4 cos t

A: Given data is : x=2+3 sinty=-1+4 cost To find the value of d2ydx2

Q: dz (2) Suppose z is a function of x and and suppose cos(32) xyz?. Find in Y, terms of x, y, and z.

A: The given function is, cos3z=xyz2

Q: - Given the function f(x, y, z) = x ln(1 – z) + and simplify your answers. a) fa b) sin(x - 1) 2y…

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Q: 1. Find the most general antiderivative of the function 12 f(x) = ( 2r + sin(4- r) + 7e

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Q: 6. If f(x,y, z) = x³y³ sin (z²)+z³ cos (x³), find an expression for fryz and evaluate it at the…

A: Given f(x,y,z)=x3y3sinz2+z3cosx3 To find: fxyz fxyz at (1,1,π)

Q: For the given function f(x) = cosx, let xo = 0, %3D X1 = 0.5, and x2 = 0.7. Find the value of…

A: From the given x=0.75, x0=0, x1=0.5 and x2=0.7. It is known that, the lagrange interplotation…

Q: %#34 For 0< 0 < 2n, find 0 such that the function is undefined. sin e cos e a) f(0) b) G(8) cos e…

A: For 0≤θ≤2π   a)f(θ)=sinθcosθ f(θ) is undefined where the denominator is equal to zero.…

Q: Solve the equation for x, where x is restricted to the given interval. y = 3 tan (2x - 1), for x in…

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Q: 1-Let :=x+iy then cosh(iz ) is equal to a-cos' y+ sinh' x b-cosh' y-sin'x e- sin' x+ sinh v d- None…

A: Let z=x+iy therefore, iz=ix+i2y=ix-y=-y+ix we know that  coshz=ez+e-z2 therefore, cosh…

Q: There is a unique point a between where the function f(x) = sin x + 2 Cos a and 4 changes its…

A: Given f(x)=sinx+12cos2x Find Concavity  and Find πa

Q: 1 = cos t and f(0) = 4 f(0) + f(0+ 2T) + f(0+ 47) ? If f(t) = cos t what is the exact value of %3D 3…

A: ft=cos t and fθ=-14

Q: The function f(x) = sin(kx) contains the point A(, -1). The function is: Oa) f(x) = sin(-x) Ob)…

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Q: IV. Suppose z is a function of r and y, and tan y2 + x² = 2*e. Solve for az dz and %3D dy

A: To solve for dz/dy and dz/dx.

Q: a- Find ?f if ?″(?)=sin?+cos?,f″(x)=sin⁡x+cos⁡x, ?′(0)=3,f′(0)=3, and  ?(0)=10. f(0)=10. b-…

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Q: 1 In order to evaluate dx, the correct substitution is V-x²–4x+21 None of these -2 + 5 sin(t) x = -2…

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Q: . Consider the function ƒ(x) = cos x − 3x + 1. Since ƒ (0)ƒ (²) < 0, ƒ(x) has a root in [o,]. If we…

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Q: Q1: Find an expression of for the function y dt 2t %3D + 3x*. 3x Q2: Find an expression of for the…

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Q: 1 The function (x) = x sin x satisfies the following equation: f"(x) + f(x) + t cosx = 0. The value…

A: solve the differential equation

Q: a² f For the function ƒ(x,y), compute Or d0 if x =r cos O and x=r sin 0 .

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Q: (c) 1. f(t) dt = In(x) cos(x)+ sin(3) L e-" f(t) dt, find f(x). You may find FTC 1 useful. sin(3)…

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Q: Match the following functions with the appropriate cross-section: I) z = (y²-1) cos(x) II) z=(x²-1)…

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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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Q: 1- Find the approximate root of the following equation f(x)= cos x – x e = 0 , on the interval…

A: Here we use Newton's Raphson method to find the approximate root.