Q1: Show that the following functions satisfy C.R.E f(z) = sin z

Q: For which x value(s) is the function f(x)=sin'(2x) defined and not differentiable? Check all that…

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Q: Find the PDE that is satisfied the following function u(x, t) = e' cos(x) %3D

A: Given function,  u(x, t) = et cos (x)  To find the partial differential equation.

Q: The function f (±) = 4 cos r+ 10z has a removable discontinuity at r 0. To remove the %3D z sin z+2r…

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Q: Q2) find the slop for the tangent of the function f (x) sin(xcos(x)) at x = 2n. %3D

A: To find the slope of the tangent of the function fx=sinxcosx at x=2π. Solution: The slope of a…

Q: Find for the following function. xp y= 3x cos x sin x dx

A: Given the functiony=3x2cosxsinx

Q: Which function is equivalent to f(t) = cos 4(t- T1/4)? *

A: Given that  f(t)=cos4(t-π\2)we need to find the equivalent equation from the given equation

Q: Q1. Differentiate the following functions with respect to x: i. y = x-% -4/x ii. y = x+Inx+ sin(3x)…

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Q: Show that the following functions are harmonic: u(x, y) = tan−1 y/x

A: u(x,y)=tan-1yx

Q: Q2: Derive the following functions 3. f(x) = 1+tanx² secx | 4. Let y = 2 cos(x) ;x = 2 tan(2t) find…

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

A: Given: f''(x)=cosx

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

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Q: Q3) Evaluate the following using simpson's rule; h=1 -5 x dx 1 sin x

A: Given integral :

Q: 1 If f(t) cos(6t), find f'(t). Use exact values. f'(t) =

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Q: Given a function f(x,y,z) = (x+1) In (10y - 6) sin (4z). Find the range of the function.

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Q: Let f(x) = In(cos(x)). For what value of c is f'l =CX + TC 1? 4. C =

A: We can solve it for the value of c as below

Q: of of and da For the function f(t,a) = sin (4rt+ 7a), find - at

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Q: Find the most general antiderivative of the following functions. (d).r(θ) = (sec θ − tan θ)^2

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Q: 5. Given a piecewise function sin t, 0st< f(t) = {0, (t, i. Express f(t) in the form of unit step…

A: Given: (i) To express f(t) in form of unit step function (ii) To find L{f(t)}

Q: a²z B. For each of the following functions z, find azz and ду? a2z дx? дудх' дхду' 1. z %3D2x? — 5ху…

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Q: The tangent line to the graph of f(x) = sin'(r – 1) is verfical at z = 1/2. Select one: a. False b.…

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Q: Q2: Derive the following functions sin2x 1. f(x) sec?x 2. f(x) = x²e*²

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Q: Show that the following functions are harmonic: u(x, y) = x

A: The given function is u(x,y)=x

Q: H. For the function f(x)= cos(ax), find all MVT Values 0<c <2 where f(2)-f(0)= f'(c)(a - o)

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Q: Differentiate the following functions: 2 a. f(0)= /1+sin' 0 sin x b. y = X+COs x

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Q: Given f(x) = x + sinx, determine all values of x in [0, 2π) where f(x) has a horizontal tangent. x =

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Q: of of and da For the function f(t,a) = sin (8rt + 7a), find %3D - at

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Q: Differentiate the following functions: 1. y = x* cos t 2. f (t) = (1 – 3t)°0s !

A: Let's find.

Q: Carefully plot the function f() = 1+ E=12(-1)"+1 sin(nx) for N = 3, N = 8, and N = 20 with r in the…

A: The graph of a function in one variable x, the function represented as f(x), can be plotted by…

Q: E. If f(x) = sin x + In x, find f'(x). Check that your answer is reasonable by comparing the graphs…

A: f(x)= sin x+ ln x So, f'(x)= cos x +1/x

Q: of of For the function f(t, æ) = sin (4xt + 9a), find and da of (Type an exact answer in terms of…

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Q: Q3) Evaluate the following using simpson's rule; h=1 S dx -5 x sin x

A: Simpson's 13rule: ∫x0xnf(x)dx=h3f(x0)+4f(x1)+f(x3)+........+f(xn-1)+2f(x2)+f(x4)+....f(xn-2)+f(xn)…

Q: Q2: check whether or not the function ( u ) is harmonic. If it is, find the conjugate function (v)…

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Q: Show that the following functions satisfy C.R.E f(z) = sin z

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Q: 14 Consider the following two functions: 1 exp dx %3D (面) e() tan (2) %3D Explain why both of these…

A: Given function is  φv=12π∫-∞ve-x22dx Let us consider  fx=12πe-x22 Then, fx is the probability…

Q: Determine the function f satisfying the given conditions. f' (x) = sin(x) cos(x) f(2m) = 8 f (x) = A…

A: f'(x)=sin(x) cos(x) f(2pi)=8

Q: Given F(x) below, find F'(x). cos (x) F(x) = (1² + 10) dt 3

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Q: Given that h(x) sin(2x + 1), determine functions f(x) and g(x) such that h(x) = f(g(x))

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Q: Q5) Find f((s) if you know that g(x) = cos(x² – 1). S(x) = 3tan(x*) at vr?

A: As per our guidelines we are allowed to solve one question at a time. Kindly repost the rest…

Q: Differentiate the following function. r(t) = (te ~!,5t In t,t sin t)

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Q: Let f(x) = cx + In(cos(x)). For what value of c is f' = 4? %3D 4 C =

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Q: Given that f (x, y) = y ln x cos x, find fæærzay (T, 1). Keep your answer to three significant…

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Q: For each of the following functions ƒ :R² →R compute at the point a. sin(x)cos(y) (a) f(x,y) = a =…

A: According to our guidelines we can answer only 3 subparts at a time, rest you can repost later.

Q: Determine the function f satisfying the conditions f'(x) f (e*) = 38 f (x) = sin(x) + 2

A: This separable differential equation

Q: b. Find y' of the following function using MATLAB y = sec(In(2M * x))e5x + cos(2Nx)

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