Evaluate the convolution, f(t) * g(t) = 8t*e', then evaluate at t = 2.

Q: 1- f(x,y) = In(x² + y?) at (1,1)

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

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

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Q: Q5/ Determine the total differential If Z = f(x,y) = x²y², x=2rcose, y = 2rsine

A: Here, the total derivative rule used is: z=f(x,y)=x2y2 & x=2rcos θ , y=2rsin θ

Q: Differentiate fx) with respect to g(x) of yx= xsiny

A: To find the derivative

Q: Find the MacLaurin polynomial of degree 7 for the function sin (ot) dt. F(X) = %3D

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Q: Find the linearization L(x) to the function f(x)= Vx+4 at x =4, then use the linearization to…

A: linearlization of f(x) at x=a is  L(x) = f(a) + (x-a)f'a)

Q: Q5/ Determine the total differential If Z = f(x,y) = x²y², x=2rcose, y=2rsinė

A: this is a problem of differential. Based on the general formula and concepts we will answer the…

Q: If fCx) is bdd Junchion an f(x) dx = の-3 then 3. True or Fal se ?

A: Solution :- An odd function is defined such that f(−x)=−f(x)

Q: Assume that f(x) is a differentiable and invertible function so that f(3) = 4 and f'(3) = .…

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Q: Find the linearization of the function f (x) = x at x = 1. L (x) = 固団 Using this linearlization, f…

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Q: Find the linearization of the function f (x) = x' at x = 1. a ab Va |a| sin (a) 7 х-6 L (x) Using…

A: Given a function,

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

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Q: Use chain rule to find express answer in terms of x only. dx y = Vu² – 1 u = 4Vx

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Q: Approximate X f(x) = e*over the interval [- 4, – 2] using 2 subintervals.

A: In this problem, Simpson 1/3rd rule is used to find the approximate value of e^x over the interval…

Q: 2. Find frxz for f(x, y,z)= z² e³xy

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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: 8. What is the relationship between a and b so that F(x, y) = (ary, 3ax + bry) is source free?

A: That's easy. Have a great day!!!

Q: Suppose F(x,y)=sin²(xy +e"), where x=u² +v and y = In(u² +v). Find the . ƏF ¸ ÔF value of when u =1…

A: The given function is: F(x,y)=sin2xy+eywhere:x=u2+v         and         y=lnu2+v

Q: Find the antiderivative of f(x). f(x) = 3e6x+ sec2(x) +x3

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Q: Use differentials to approximate V36.1. 3.

A: Consider y = root x.Let take x = 36 and delta x = 0.1.Find delta y as follows.

Q: Use the General Power Rule, Exponential Rule, or the Chain Rule to compute the derivative.

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Q: Find the linearization L(x)of the function at a .

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Q: Eliminate the arbitrary constants a. x = -In t, y = at + bt?

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Q: Find the linear approximation of f(x) = (5 + x)n at x = 0. Use the approximation to estimate the…

A: fx=5+xn at x=0. Differentiating with respect to x, we get f'x=n5+xn-1 Now, f0=5+0n=5n &…

Q: In integrating the function fx* in Sx dx using integration by parts, what would you choose for your…

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Q: Find the best linear approximation to f on th e interval [0, 1].                            f (x)…

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Q: 3.Find the linear approximation to f(x) = cos x at x, = ÷ and use the linear approximation to…

A: We will use formula for linear approximation.

Q: (b)Assume that f(x) is a function of the form -x-1; when -T < x <0 f(r) = when 0 <r < T Prove…

A: For the solution of the problem follow the next step.

Q: Find the zeYo k its ovdev for Sunction f2)=1-Ti + Z+ e.

A: Given the function, f(z)=1-πi+z+ez. Now, in order to find the zero of the function f(z), we will…

Q: Find the local linear approximation L (x) of the function f(x) = 5 – x² at =2.

A: To find the linear approximation of given function.

Q: Find the linearization L(x) of the function at a. f(x) = sin(x), a =. 3 L(x) =

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Q: Find the linearization of the function f (x) = x° at x =1. L (x) Using this linearlization, f…

A: To find the linearization of the following function

Q: lim, f(x)= 0, then | f(x)dx diverges

A: Statement:  limx→∞ f(x)≠0,  then ∫1∞ f(x) dx   diverges.

Q: d Use the chain rule to calculate f(x) if f(x) In (1+ tº) dt. dx, 0. f(x) =

A: let's use chain rule and find derivative of integral.

Q: Find the derivative. |4t +5 dt O A. V4x+5 O B. V4x+5 - 5 2 OC. V4x +5 OD. (ax + 5)/2

A: It is given that, y=∫0x4t+5 dtWe have to find the derivative.

Q: Evaluate the implicit function by finding dy/dx of x³+3y=3xy

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Q: find ∇f at the given point. ƒ(x, y, z) = x2 + y2 - 2z2 + z ln x, (1, 1, 1)

A: Given function is fx,y,z=x2+y2-2z2+zlnx and point=1,1,1

Q: Find the linear approximation L(x)of f(x)=x^4 at the point a = −5 L(x)=

A: Given that f(x) = x4 We have to find the linear approximation L(x) of f(x)=x4 at the point a= -5.

Q: Find the linearization L(x) of the function at a. f(x) = sin(x), a = 3 L(x)

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Q: - Given f(x, y, z) = x In(yz³), find fzy and fyz.

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Q: df Find dx by using chain rule if f = u =-1 , x=-1 u+1

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Q: Find the linearization L(x) of the function at a. f(x)= sin(x), a= π\4

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Q: Find the linearization of the function f(x)=x5 at x=1. L(x)= Using this linearlization, f(1.04).is…

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Q: (b). Examine the behavior of e*+iy as x → -.

A: Euler's formula states that for any real number x  Any complex number z = x + iy,  can be written…

Q: of of For the function f(x,y) = In (x+ 3y), find and dx df of ду II

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Q: Find L(x) (Linearization function), given f(x) = ev2x at the value a = 2.

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

A: