Compute r"(t) and r(t) for the following function. r(t) = (cos 2t, sin 3t, cos 6t)

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

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Q: Let V = eP cos(qr), with p = x In(xyz), q = z cos(Ty) and r = 2 tan-(y). By using the chain rule,…

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Q: Q2/ find dz ond dZ as function ne U and v if of Z=tan (중), X=u Cos V , 9-u sinV

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Q: Find g'(x) if g(x) = t² cos 6t dt %3D 2

A: We can apply fundamental theorem of calculus here.  The second fundamental theorem of calculus…

Q: Find r(t) for r'(t) = 2Vti + 3 cos(2nt)j- e-'k and the initial condition r(0) = i+ 2j.

A: Solution is attached

Q: Transform F(s) (giving you cos 5t + t³

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Q: Compute r'"(t) and r'(t) for the following function. r(t) = (cos 5t, sin 2t, cos 3t) r'() = (ODD

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Q: Q1. If f(x.y,z) = cosh²(\x² In y) + tan-(ey*NE) + sec*(sin Vz In x²) Find fx, fy, fz fyx

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Q: Compute r' (t) and r'"'(t) for the following function. r(t) = (cos 4t, sin 3t, cos 2t) %3D

A: If, r(t) =<f(t),g(t),h(t)> , where f(t), g(t) and h(t) are differentiable functions,   then…

Q: f(x) cos (at) if t 20 %3D 0 if t<0

A: Given: f(x)=cos αt if t≥0o if t&lt;0

Q: ds The function satisfying - = 4 +7 cos t and s(0) = 7 is s(t) = dt

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Q: /hich of the following does not require the use of the dy nain rule to find ? dx A y = cos1 (10x –…

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Q: The integral cos(x – 3) dx is transformed into , g(t)dt by applying an appropriate change of…

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Q: Compute r"(t) and r""(t) for the following function. r(t) = (cos 4t, sin 2t, cos s 6t)

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Q: a. The velocity of a car in meters per seconds travelled from its origin is given by v(t) = In (t2 +…

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Q: Find the linear approximation to g(z) = cos(z + 1) at z = 0. Use the linear approximation to…

A: The formula to find the linear approximation Lz of a function fz at the point z=z0 Lz=fz0+f'z0z-z0

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: If f (x)= [a(«) =os* '(5) [1+ sin(t?)] dt find f 1 dt, where g(x) V1+t3 COS X

A: We need to find value of derivative.

Q: Find for THREE of the following functions: dx 1-y()+In(cos(x)) + √2-y=2(cos(x))*(x)

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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: The value of f(z) = e² at z = 3 + 4i in terms of x + iy is O a. 1 O b. e cos 4+ie sin 4 O c. e*…

A: Given, We have to find the value of  fz = ez  at  z = 3+4i  in terms of  x+iy  .

Q: ds Find the function s(t) satisfying = 4 -9 cos t and s(0) = 7. dt

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Q: Calculate L4 for f(x) = 24 cos () over %3D LA

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Q: Which of the following is equivalent to u=-cost+v3 sint ? a) u = 2 cos t +- 1 b) u = – cos| t+ 2 3…

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Q: 2. F(x) = fr Cos t dt %3D

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Q: Q1. If f(x,y, z) = cosh?(Vx² In y) + tan-(e2y²vz) + sec³(sin vVE In x²) Find fx, fy, fz» fyx

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Q: Find a function f that satisfies the equation | f(t) dt = 2 cos x + 3x – 2. %3D -

A: Derivative of a definite integral is: ddx∫0xf(t)dt=f(x) Formulae used: ddxcosx=-sinxddxx=1ddxC=0…

Q: Let C be defined by 7(t) = |cos (t), sin (2t), t²| for 0 < t < n 2 sin(Vz) 9x*dx + 2zdy + + 2y ) dz…

A: Using the result that  ∫cF·dr=∫cPdx+Qdy+Rdz=∫P(r→(t))dxdt+Q(r→(t))dydt+R(r→(t))dzdt dt Here,…

Q: r(t) = (4 sint- 4t cos t,4 cos t+ 4t sin t), for 0sts, 2

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

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Q: f(t) = et+1 cos t. f(t) = eat43/2_ f(t) = eat cos 3t.

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Q: 3. Let V = e" cos(qr), with p= r In(ryz), q = z cos(ry) and r = 2 tan-(y). Ae when r= y = 2 = 1. By…

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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: Answer

Q: Compute r" (t) and r"(t) for the following function. r(t) = (cos 3t, sin 6t, cos 2t)

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Q: If x = 2 sin* t and y = 3 cos* t, then find dy at t = %3D dx 4 а. 1.5 b. -2.5 с. -1.5 d. 2.5

A: Solution:

Q: f(t) is given by: 3t for 0 = 2.

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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: Find the convolution of f(t)=cos(t)f(t)=cos(t) and g(t)=cos(2t)

A: Given function is f(t)=cos(t) and g(t)=cos(2t)

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

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Q: Given f(x,y) = ex cos y, Evaluate fy(0,2) A cos 2 B) e² CO (D) -sin 2

A: This question can be solved using the concept of partial derivatives.

Q: 2 tan-1(y). x In(xyz), q ƏV when x = y = % = 1. ду Let V = eP cos(qr), with p = z cos(TY) and r = By…

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Q: Find a trig substitution r = f(@) that makes 1 dr = cos 0 de. (V4+)3

A: Here we have to substitute x =f(θ)

Q: Find a function f such that ∇f = ex cos yi − ex sin yj + zk.

A: Given, ∇f = ex cos yi − ex sin yj + zk.

Q: 5. Find Sp√x² + y² dr, where ř(t) = t cos t tsint Ost), 0 ≤t≤ 2π.

A: Given r→(t)=tcosttsint,0≤t≤2π. The objective is to find ∫Px2+y2dr.

Q: ds Find the function s(t) satisfying = 6 +5 cos t and s(0) = 5. dt

A: It is integration using initial conditions.

Q: The integral . (cos(3x))'sin(3x)dr under the change of variable u = cos3r becomes v u'du. 9/29

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Q: H.W- Compute y( E) with y-J = -8(Sinx+ cosX) 9(T)=0, ý(T) = -8 %3D

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Q: Is this correct?

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