Use the convolution theorem to obtain f(t) if : 3.1) F'{F(jw)} = %3D 7+ 8iw-w?

Q: If z = xe" and x = t2, y = Vt then the value of dz at t = 1 is equal to . dt Select one: True False

A: Solve the following

Q: Can you explain the question step by step

A: Given: z = f (x,y) , x= e^s.cos(t) ,  y= e^s.sin(t)

Q: f(x,y) = =dt V11-6t?

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Q: 2. Show that the function u = p(xy) + Vry v(y/x) provides the equation = 0. dy? | dx²

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Q: 2 consider, Differentiate with respect to x', dy C」.2ス %3D de

A: From the image , two find a differential equation eliminating the constants from the given relation.…

Q: dy sec (re ), y(In 4) = 3 / t dt

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Q: Consider w = x² – y², where x = s cost and y = ssin t. Find u and hu using the Cha dw at ds Rule.

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Q: Compute DF(, ) of F(1, y) = (e" cos(ry), r² + y) %3D

A: Given function is F(x,y)=eycos(xy), x2+y Let  f1(x, y)=eycos(xy)f2(x, y)=x2+y

Q: Q2/ by using chain Rule to find dw at t = 1 if dt w = 2ye* – Inz ,x = In(t? + 1), y = tan 1t,z = et

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Q: What is the maximum value of f(t) = sin t + cos t in the interval 0<t< =?

A: Given; f(t) = Sin t + Cos t.

Q: Given f(z) = | t2 – 16 dt 1+ cos²(t) OS At what value of a does the local max of f(x) occur?

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Q: Get z = f(x,y), x = es cos t, y= es sin t 2 + əx. 2 2 Show that it's + at. as

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Q: Given f(x, y) = 3æ'y- 8ry. Compute: www dy?

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

Q: dy for y= In(In(2r')) dt

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Q: dy For the function dt d y is 3 cos t, the third %3D order derivative dt3 O 3 cos t

A: Given: dydt=3cost To find the third order derivative d3ydt3. Solution: We have, dydt=3cost…

Q: Suppose that a = x(t) and y = y(t) are both functions of t. If y + xy – 3x = 23, and dy/dt = 1 when…

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Q: S. Find f(t), if f'(t) = df 1+ cos(2t) and f =1. %3D %3D dt

A: To find the function f(t) following the given conditions.

Q: dy/dt= 2e-t/8, t is greater than or equal to 0

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Q: Find dy/dt of y = Ssin (cost) and simpli -t -cos t cos t V1-? the

A: Given:- y=sin(cos-1(t))  To find:- y'

Q: COS. dt, for alla at, for all r 58 1 dt 58. for |x| < 1 (1 – t4

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Q: Show that the function y(x, dy/at = a2y/ar2 = dy/ax = %3D %3!

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

Q: find given f (x, y) = eª + 2xy² – 4y at (0, 3) af dy'

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Q: Given: y=fso(x-1) dt - dy =D{(x). dx show that

A: We will prove the following result using Leibnitz rule.

Q: dz If z = e2x+ 3y and x = In t, y = t2, calculate from the total dt derivative formula and show that…

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Q: The linear approximation at z = 0 to sin(4z) is A+ Bz where A is: and where B is:

A: Linear approximation is found by L(x)=f(x)+f'(x)(x-a) Differentiate L(x) with respect to x.…

Q: The linear approximation at x = 0 to sin(2x) is A + Bx where A is: and where B is:

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Q: Suppose that w = xe"/, where x = t², y = 1 – 6t, and z =1+ 4t. dw Find dt

A: w=xeyz, where x=t2 , y=1-6t and z=1+4t

Q: 2. If f(x,y)= te Vy of=D0 then show) that 49 c) of af =0 dxay

A: Consider the given function. fx,y=1yex-y24y (i) First, we have to show that ∂2f∂x2-∂f∂y=0. First,…

Q: Find the length of the curve y = V cos 2t dt from x= 0 to x = 4

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Q: Find an interval where the IVP dy (In t) + y = cot t dt y(2) = 3 has a unique solution.

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Q: Let f(x, y) = 7e2" sin(5y) af af dy

A: We can make it easier for you

Q: of find 4x + 9y of and dy For the function f(x,y) = %3D of dx ||

A: We can answer this question as below

Q: Find the orthogonal trajectories of r^n= a^n cos . given that r(1) = 13

A: Hey there since you haven't mentioned any angle of cos therefore i am assuming it to be cos (n…

Q: Q1: Use Green's theorem to evalute S. (xy + y2)dx+ x?dy by the curve y = x and y = x2.

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Q: Suppose that r = x(t) and y = y(t) are both functions of t. If %3D y = 2x/2 + 3, and dx/dt = 5 when…

A: The given function is: y=2x12+3

Q: (1, y' + 5y = f(t), y(0) =0, where f(t) = 0st<1 %3D t21

A: Solve the intial value problem using Laplace transferoms

Q: Use the Linear Approximation off (x, y) = ex2+Y at (0, 0) to estimate f (0.01, -0.02). Compare with…

A: By the method of linear approximation, if we are given a differentiable function f in two variables,…

Q: Evaluate dt dW at t=0 for the function W = e' – In x , x = t², y= In t

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Q: aw nd dt in term of t, if w = xy, x = cost and y = sint, when t = - %3D

A: Question 4 is not complete.  I am answering Question 5.

Q: Let f (x,y) = sin(xy) + x² ln(y). fyx at (0,) is equal to: %3D А. 33 В. О С. 3 D. 1

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Q: Find fr and fy- f (x, y) = 8e dt

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Q: Integrate from f(x) = x4 from 0 to 1 by (Trapezoidal Rule) with h = 1, h = 0.5, h = 0.25 and…

A: Here, f(x)=x⁴ So, I=  Integrate from f(x) = x⁴ from 0 to 1. Now we can solve by Trapezoidal rule,…

Q: a. Apply the Runge-Kutta method of 4th order to find the approximate value of y for x =0.2, dy in…

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Q: Suppose y = (sq. root of) 2x + 1, where x and y are functions of t. (a) If dx/dt = 9, find dy/dt…

A: y=2x+1 Differentiating with respect to t, we get dydt=122x+1·d2x+1dt…

Q: Find the directional derivative of Du f(2,1) in the direction of: d = 7i + 2j To f(x, y) = In(Ges…

A: As per our guidelines we are supposed to answer only one question. Please repost another question as…

Q: Find f, for f(x, y) = | cos(r*) dt.

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Q: (b)/ Use the Trapezoidal Rule with n = 4 to estimate ſ,(x3 + 1)dx.

A: To find: ∫-11x3 + 1dx using trapezoidal rule with n=4

Q: By differentiation show that ∫ f(s)ds    +   ∫g(v)dv     =  0  (to to t)        (yo to y) becomes…

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