Find the convolution f(t) * g(t) for the following problem. f(t) = g(t) = 3 sin t (f * g)(t) =|

Q: For each of the following exercises, a. decompose each function in the form y = f(u) and u = g(x),…

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Q: If f(x.y) = In(x² + y²) + find fr and fy -

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Q: 4. Find the linear approximation to f(x) = cos(x) near a =- [Where L(x) = f(a) + f'(a)(x – a) ]

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Q: For f(x) = e+cos(x), calculate f (0) by using the chain rule!

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Q: Solve for F(s): 01

A: Given function is ft=0,      0<t<1t,        t>1             ...(1) To find: Laplace…

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A: Given query is to solve the differential equation.

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Q: -Find the D.f ofr (x, y) = (x² – y)' at Po(3, 1) with

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Q: Find F(s). F(s) = £{t¹8e-4tz X

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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: Consider the function f(x) = a²e15z. f(x) has two inflection points at x = C and x = D with C < D…

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Q: af dy of f(x, y) = tan (x²y³ + 2xy)? What is the

A: Given:     To determine:

Q: 1. If f(x, y)=3x' cos y– y sin x– 2.x In y- yln x-4x²y, find ôf ôf d²ƒ _ô²ƒ

A: According to question given thatf(x,y)=3x3 cosy-y2 sinx-2x ln(y)-y ln(x)-4x2y

Q: COS Z fined the Res of the function T Z 4 -

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Q: d Use the chain rule to calculate f(x), if f(x) dx, dt. -x12 f(x) =

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Q: of and dy For the function f(x,y) = In (8x + 9y), find - - of

A: partial derivative of two variable functions

Q: f(2) = | : t2 – 1 dt 1+ cos² (t) At what value of ¤| does the local max of f(x) occur?

A: Given that a function f(x) and we find value of x does the local maxima of f(x) occurred. We know…

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

A: To calculate the approximate value of a) f(1.9) and b) f(2.04)

Q: Find the linear approximation L (x) to ƒ (x) = xcosx at a = T.

A: Given that, f(x) = x cosx and we have to find linear approximation L(x) at a = π

Q: For the relation siny – y² =x²y– x+x , is dx 3x²y+1 А. cos y – 2y –x T – 1 3x² + 2y – cos y cos y –…

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Q: Find the linear approximation to f(x) = cos(x) near a =- [Where L(x) = f(a) + f'(a)(x – a) ] 3

A: Solution: The objective is to find the linear approximation

Q: 3. Let X(t) = t2W (t) – 2 f sW(s)ds, Is X(t) a martingale?

A: X(t)=t2W(t)-2∫0tsW(s)dsWe know that, X(t) is a martingale, if,EX(t+1)=X(t)

Q: f(x, y, z) = e2* +e3y + e4=

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Q: t² – 4 - 4 f(x) = -dt 1+ cos²(t) 0.

A: Given:  f(x)=∫0xt2−41+cos2tdt

Q: If F (x) = (t2) dt , then F' (4) = cos 0,

A: DUIS rule is used

Q: d) The function +(xy)-r*r2y) exp G 18xy is homogencous in of degree X and

A: The given function is: f(x,y)=(x2+2y)e2xy+8xy...(1) The function f(x,y) is said to be homogeneous…

Q: For the functions w = 8x + 3y, x= cos t, and y = sin t, express dw as a function of t, both by using…

A: The given function is w=8x2+3y2, x=cost and y=sint. We have to express dwdt as a function of t.…

Q: For ey – In x=y2, find the value of so that & (y' – y') = 1 at y =0- O e e

A: we have to find

Q: ) Find f(t) if f(t) dt : = x sin 6x. A) 0 B) 6 C) n D) 6t

A: According to function,∫0xft dt = x sin 6x

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: Find the vertical trace of the function at x = 1: g(x, y) = cos√x² + y²

A: Definition : Consider a function z=f(x,y) with domain D⊆R2. A vertical trace of the function can be…

Q: Finf y' if x=Arccos(1-t), y=/2t-t2.

A: We can find the answer using chain rule as below.

Q: Find the differential of the function. z = 7t − 7/t2

A: zt=7t-7t2

Q: - The antiderivative of f (x) =; whose graph passes through the point (C 3+5sinx+. +3cosx 1(. 5 1(.…

A: Introduction :

Q: If sin(x) f(x)= V2+t2 dt tan(x) and g(y)= f(x) dx g" (4) Then is equal to V5 - 2 V3 - 2V3 11 E- 2V3…

A: Given:            f(x)=∫tanxsinx2+t2dt  and g(y)=∫1yf(x)dx

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: Q3) For f(x,y) = Sin(x,y) find fryxy at (1,–). %3D

A: Given query is to perform indicated derivative operation.

Q: Find the linear approximation at x = 0 to each of f(x) (x + 1)?, g(x) = 1+ sin(2x) and h(x)= e2*.…

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Q: For y=f(x)=x²-2x+7, find dy and Ay, given x=4 and Ax= -0.2. dy=(Type (Type an integer or a decimal.)

A: Use formula and put value

Q: Find the Giniindex for the lorenz curve L (X)= 0.3X + O=7X 11

A: Given the Lorenz curve Lx=0.3x2+0.7x. Find the Gini index of the Lorenz curve.

Q: Find the gradient ∇f of the function f given the differential. df=2ye^xdx+xe^xdy   ∇f=

A: Note that            . Here, df=2yexdx+xexdy. So, here we have fx(x, y) = 2yex and fy(x, y) = xex.

Q: Find the differential dy of each function: a) f(x) = 2x^1/3 - 3x^1/2 b) f(x) = ( x^2 +1) / (x+1)

A: we will find the derivative of given function using basic differentiation rules.

Q: for the function f(Z) z²-2z find the (z+1)° (2 t4) residues at singular points.

A: The residue of f(z) is solved below

Q: Let f be the function defined as follows. y = f(x) = /7x + 6 (a) Find the differential of f.

A: Given data: The given function is y=(7x+6)1/2.   (a) The expression for the derivative of the given…

Q: 2. If g(x) = x + 2 cos x, then the equation of the tangent line to the graph of g at x = is A. 2y +…

A: Wr have to find the derivative of the given function first.

Q: Use the Quotient Rule to compute the following: t2 + 1 at t = -2 dt \ t2

A: