Match functions a-f with the appropriate graphs A-F. a. r(t) = (t, – t, t) c. r(t) = (4 cos t, 4 sin t, 2) e. r(t) = ( sin t, cos t, sin 2t) b. r(t) = (r², t,t) d. r(t) = (2t, sint, cos t) f. r(t) = ( sin t, 2t, cos t) %3D

Q: 2. Find the function that satisfies these conditions: 7 (t) = (e', sin t, sec² t); 7 (0) = (2, 2, 2)

A: Ffff

Q: (c) For a differentiable function f(x, y) with x = rcos0 and y = r sin0; (i) Draw the Tree diagram.…

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Q: 5. Find a function u(r, 8) that is harmonic outside the unit disk, equals f(0) = 2 sin(30) + 4 cos…

A: In the given problem we used the fact that f is harmonic on the unit circle, and using the…

Q: Let f (x) = 3 sin(4x) Find the values for the constants in the derivatives f' (x), f " (x), f '"…

A: I will differentiate the given function to find required constants

Q: (c) x(t) = eat cos s wtu(t), a > 0 (d) x(t) = e-af sin w,tu(t), a > 0 %3D

A: Let xt is a function. The Fourier transform of the function xt is denoted by Xiwor Xf and defined by…

Q: Given f(x,y,z) = cos(4xy) + sin(4z). Find f,(8,9,0). Leave your answer correct to two decimal…

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Q: eliminate the parameter to find an explicit equation for y as a function of x.  x = 1 + 3 cos(t) y…

A: Given,          x=1+3cost          y=-2+4sint

Q: Let y = (sin x+ cos r)e , x E 0, 27. Then the x coordinates of the inflection point(s) of this…

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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: One of the followings is a harmonic function O a. u(x,y)=(x' - y' – 2x+1), O b. u(x,y)=(x-y - 2x+1),…

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Q: Find f. f '(t) = 4 cos(t) + sec2(t), -r/2 < t < t/2, f(T/3) = 4 TC + tan 3 +4 -3/3 3 TC f(t) = 4 sin…

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Q: Find a and b such that f is differentiable everywhere.

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Q: 1 a²E(x,t) _ 0: a²E(x,t) əx² x E (-00, 00), t e [0, 0) c2 at2 ƏE(x,0) E(x,0) = sinx, = cosx at

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Q: (a) Find a function f(x) satisfying the conditions f' (x) = cos(x), f(0) = -2, f' (0) = 6, f"(0) =…

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Q: 1. Find the absolute extrema of the function f(r) = e sin r-sin r+cos z in the interval [0, "]. %3D

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

A: As per the answering guideline, only one question can be answered at a time. Please repost the other…

Q: 13. The function y = In sinx, when differentiated is? B. COS X A. cot x C. sec x D. tan x 15. The…

A: Given: y=lnsinx, y=sin23x

Q: f(t) dt = tan x. cos t %3D Find a function ƒ and a number a E (-5, 5) such that 1+ a

A: Lebnitz theorem

Q: Given f(x,y,z) = cos(3xy) + sin(3z). Find f,(8,2,0). Leave your answer correct to two decimal…

A: Partial differentiation of f(x,y,z) with respect to x is calculated by treating y and z as…

Q: Consider the function given by y = cos(bx) on the interval (0, 2). (a) Sketch the graph of y =…

A: Introduction: The cosine function is a significant trigonometric function. It is a periodic function…

Q: Z-T 4. Find all singularities in C for the function f (z) and their residues. sin? z

A: We can solve this question using definition of singularities and residues

Q: Using modified Euler's Method to Find y (0.2) to the function 5x+cos(y) f (x, y) where h=0.1, y (0)…

A: We need to solve the given function using modified Euler's method. We need to find y(0.2) given that…

Q: -cos x + sin x in the form r sin (x + a), where r> 0, is: e A. 2 sin x+ -sin |x+ 4 B 57 2 sin x+ 4 2…

A: We will find out the required expression.

Q: (i) Let f(x) E[an cos(n7x) + b, sin(nax)] , %3D where, | +x, -n <x< 0 | 0, f(x) = 0 < r<T. Then, b,…

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Q: Find an equation of the tangent line at the given point on the curve. (a) x = 2 – 3 cos 0, y = 3+2…

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Q: 7. Find the value c that satisfies Rolle's Theorem for f(x) = cos x on A. T/2 В. "/4 C. 3/4 D. 0 Е.…

A: In this question we will use basic of calculus i.e concept of Rolle theorem. We will use Rolle…

Q: a) The tangent line for y = f(z) at the point (c, f(e)) has as its equation y = f(c) + f'(e)(r – e).…

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Q: u(x,у)- (sin x)(e' — е").

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Q: iven po r (t) = (sin (t), cos (t), In(cos (t))), (0, 1,0). T = 1 1 1 - N = V2 1 1 B = V2

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Q: (b) Find 7, T, N, and B at the given value of t for F(t) = (cos t)î + (sin t)ĵ – k, t=. 4

A: According to bartleby guidelines I can only answer the first 3 sub questions of the given problem.

Q: 20. Let h be the function defined by h(x) = [", sin²r dt. Which of the following is an equation for…

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Q: Find the absolute maximum and absolute minimum values of f on the given interval. f(t) = 2 cos(t) +…

A: Consider the given function. Differentiate the above function with respect to x. Equate the above…

Q: Given a function of two variables f, let the single-variable function g be defined by g(t)=f(e^t…

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Q: cos x+sin x-e 2 cos x-2 cosh y If f (z) = u + iv is an analytic function of z and u-v = prove that…

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Q: Find the length of the curve over the given interval. =8 r = 7(1+ cos 0), 0 <0< 2n

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Q: For which values of t is the curve concave upward? x=cos(2t) y=cos(t)

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Q: Suppose a particle begins to move from the origin(t = 0) following the curve in space. r(t) =…

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Q: Let f(x) = 5/2 cos x and let a = 4 Complete parts (a) through (d) below. a. Find the linear…

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Q: Find f. f"(8) = sin(e) + cos(e), f(0) = 5, f'(0) = 4 f(e) = 5t – sin (t) – cos(t) + 6

A: Here we have f''θ=sinθ+cosθ, f(0)=5, f'(0) = 4 fθ=?

Q: Find the absolute minimum and absolute maximum values of f on the given interval. ft) = 4 cos(t) + 2…

A: This question is related to trignometry, we will solve it using differentiation.

Q: Find the function r that satisfies the given condition r'(1) = (e!,c . r(0) = (5,5,5) Cos t, sec…

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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: 4 sin z Let f(x) 2 sin a + 4 cos a Then f'(x) = %3D The equation of the tangent line to y = f(x) at…

A: Given fx=4sinx2sinx+4cosx

Q: The conjugate harmonic function v(x, y) of u(x, y) = In (x2 + y2) is *(;) + -1 1. 2tan () + -1 2tan…

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Q: Consider the function. y = -7 sin-(x) (a) Decompose the function in the form y = f(u) and u = g(x).…

A: We have a function to find part (a) and (b).

Q: dy when (cos x) = (sin y)* dx A Find %3D

A: Note: - Since you have asked multiple question, we will solve the first question for you. If you…

Q: Let F = Vo where o = e cos (Vy - a). If C is the cardioid defined by ((2+ sin 0) sin 0, (2 + sin 0)…

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Q: Let f(x) = 3 sin'x - 7 cos(2x), 0 <xS T. Find the interval(s) on which f is increasing. (A) (0, 7)…

A: Recall that, f is increasing on (a,b) if f'(x)&gt;0 in (a,b).

Q: We have r(t) = (2e-t, sin-'t, In(1 –t)) , %3D Find 1- The domain 2- ar , an, T, N and t at t=1

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