Consider the function f (2) = e7². Show that if f (2) is purely imaginary, then 2n + 1 = Z 14 -T, n = 0, ±1,±2, . ..

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: 1. Find the convolution of f(t) = 3t and g(t) = sin2t?

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Q: Given t2 – 4 f(x) = dt 1+ cos2(t) At what value of x does the local max of f(x) occur?

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Q: 3 Let f(x) = 2 + In(bx), where b is a positive constant. Find f'(x).

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Q: a2f b- For the following functions prove that ax2 ay2 1- f(x,y) = e-2y cos 2x %3D f(x,y) = In/x2 +…

A: The first step inludes the  partial differentiation of the functions individually with respect to y…

Q: dy from t dx n for y as a function of x, and find two results are consistent by expressing the (a)…

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Q: 4. Find if y is a function of r defined implicitly by da 2*y + sin a = xe" + In

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Q: hich z ∈ C the function e^(1/z) is holomorphic?

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Q: Show that E [x(t)] = 0. %3D

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Q: Find the Wronskian for the set of functions.{e3x, sin 2x}

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Q: For the function f(x,y)= (x² + y²) tan(ln(xy)) + e(x-y) which of the following is the value of…

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Q: The function g(x) = ln(x³ – 1) defined on V2, 0) is not zero unless x 2.

A: Given statement

Q: Q2/Show that the functions is harmonic u = 2 x (1 - y)

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Q: Differentiate the function with respect to the independer X f(x) = +e5x + e 2 e (x) = 0

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Q: For the function f (x) = cos² x – 2 sin x, find the interval(s) on which f (x) is…

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Q: 3. Find the constant k that will make f continuous on (-0o, 00). Sx – 4 , (kx2 – 24x + 46, x > 5 x<5…

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Q: Consider the function f : RH→ R defined by f(x) = 2e(2z+5) log(2r+5) + If f convex or concave ? Why…

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Q: Let f(x) = cos(x). (a) On [0,2n) solve f(x) = 0. 4.

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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: Find the function f(x) and all values of c such that

A: To find the function f(x) and all values of c such that∫cxf(t)dt=x2+x-2

Q: Given f(2) = , 1+ cos (t) = |. t2 – 16 dt 1+ cos²(t) f(x) : %3D At what value of x does the local…

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Q: Differentiate the function. y=In(x²+e' y=In(x²+ean x)

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Q: Prove that the following function is harmonic and obtain its harmonic conjugate function: u(x, y)…

A: Introduction :

Q: Find x' for x(t) defined implicitly by x+t°x+t -8=0 and then evaluate x' at the point (-2,2).

A: x3+t3x+t4-8=0Differentiate w.r.t…

Q: find the aradients of the functions below a)f(x, y) = e-3y cos4x

A: We have to find

Q: 9. Suppose f(x) is continuous and f(x)dx = 10, f(x)dx the equation f(x) = 1 has a solution on the…

A: Divide the interval [-5,5] in to two sub intervals [-5,-1] and [-1,5]

Q: Find of the function f(x,y) = sin(x²y³). əx3

A: The product rule of differentiation : (PQ)'=PQ'+QP' sinx'=cosxcosx'=-sinxxn'=nxn-1 Use the given…

Q: If u = f(x), then f- dx ++2x+1 +C for some constant k. Compute kf(1).

A: In this question we have to compute kf(1).

Q: The function f(z) = 1 has a poles at z = %3| ez – 1

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Q: Find the orginal function of this A Fx) =-1 (B) Frz)= X +1 ニー re Fez) s -x+3 tan x - sec3x

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Q: Compute the convolution f(t) * g(t) for f(t) = e-3, g(t) = 2t.

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Q: sketch the graph of the given function on the interval t ≥ 0. 3.g(t)=f(t−3)u3(t),where f(t)=sin t

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Q: Determine a, for the periodic function f(t)= 2t, 0<t<2n, f(t+2n)=f(t)

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Q: Supposed that z is defined implicitly as a function of x and y by the equation x2 + y2 +z2 = 4. Find…

A: The given data is: x2+y2+z2=4 To find the value of dzdx

Q: 2. If f(x) = 2x – 1 and p(x) = = cos (x). Find x, for 0 < x < 2n, if (f •p)(x) = -2

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Q: find where f'(c)=0 f(x)=-cos4x

A: Given, function

Q: V3 Find the exact values of s in the interval [0,2x) that satisfy the condition, sin s = -

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Q: Q3) for f(t) = sec-(6t- 1) and g(t) = tan (6t - 1) show that s'() = g'(t). %3D

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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: The function f : XI→ a + b cos x, is defined for 0 sxs 2n. Given that f(0) = 10 and that f (n) = 1 ,…

A: The range of a function is the values that can be obtained from the function by substituting all the…

Q: B) f(x) = x+3 (-6, 6<x<1 Is f cont. at x-6?

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Q: Consider the function f(x, y) = 3 x² y + cos(e*"). Which one of the following is correct- Oyfx-x…

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Q: The following table is used to find the root of a non-linear equation of f(x) = (cos x) – 2xe*. i…

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Q: Given x² + 13x + • 40 f(t) = 1+ cos2(x) At what value of t does the local max of f(t) occur? rp- t =

A: Here, the given function is: f(t)=∫0tx2+13x+401+cos2xdx

Q: Use differentials and the graph of f to approximate    (a) f (1.9) and (b) f (2.04).

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Q: If f is a quadratic function such that f(0) = 9 and f(x) x2(x + 1)3 dx is a ratianal.functian,,find…

A: This question is about finding f'(x)  at x=0  where f(x) is a rational function