the guotient f(xth) f(a) where h is cortont.

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

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Q: Find the antiderivative F of f(x)=4-3(1+x^2)^-1 that satisfies F(1)=-2.

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Q: Show that the function f(x) = e¯*/2 has inflection points x = f1. at

A: We have the given function as fx=e-x22              ⋯⋯1 As we know that, a point of inflection of…

Q: : Apply Rolle's theorem for the function f(z) = 7x² – 28z+ 21 over the interval [1,3]. er.

A: The given function is, f(x)=7x2-28x+21 over the interval [1,3]. Observe that, the given function…

Q: the function f is not differentiable at x=0.

A:

Q: 3 Let f(x) = 2 + In(bx), where b is a positive constant. Find f'(x).

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Q: – x®y³, 6. Given f(x, y) = e®° - show that fxy = fyx.

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Q: Find the particular antiderivative F(x) of f(x) = x6 1 that satisfies F(1) = 4. - %3D

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

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Q: If f"(x) = V - cos(x). f'(0) = 2, and f(0) = 0, find f(x). %3D

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Q: 2. Let f(x) = S dt for x 2 2 In a) Find F'(x). b) Is F increasing or decreasing? What can you say…

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Q: Find linearization L(x) of f(x) = tanh=' at a= 0 and use it to estimate f(0.01).

A: Topic:- linearisation

Q: - Find the Linearization of f (x) = sinx at a 5. Provide your answer as L(x) =? %3D %3D

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Q: Explain why f (x) = sin (x² + 3r + 1) is a continuous function for all c € R. %3D

A: Let us assume that: g(x)=sin(x)and h(x)=(x2+3x+1)So,…

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

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Q: 2. k) Show that fe2) = function is analytic %3D t'+s for Rez 70.

A: Calculate the limit: lim∆z→0fz+∆z-fz∆z=lim∆z→0∫0∞e-tz+∆zt2+1dt-∫0∞e-tzt2+1dt∆z…

Q: What does it mean for f to be differentiable at a ?

A: we have to define that what we mean by the f is differentiable at a.

Q: Differentiate the function with respect to the independer X f(x) = +e5x + e 2 e (x) = 0

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Q: Find the denhetive f fue function: In(G at

A: Explained below

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

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Q: 3 ) Express f(t) in terms of the unit step function u(t).

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Q: What is the linear approximation of the function f (x) = e x at x = 1?

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Q: Consider the function f : RH→ R defined by f(x) = 2e(2z+5) log(2r+5) + If f convex or concave ? Why…

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Q: B1. Verify fy = fx for the function f(x,y) = ln(2x- 3y). %3D xy

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Q: of For the function f(x.y) = In (x + 6y), find- of and dy

A: It is partial derivative so when we differentiate with respect to one variable consider other…

Q: the function f (2) = z Cos z ̟has a zero of order

A:

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: 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 linearization L(x) of the function at a. f(x) = sin(x), a 6

A:

Q: attached

A: Linearization of f(x) at x=a is given by

Q: Find the best quadratic approximation to f on the interval [ -1, 1].                     f(x) = lxl

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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: Find the linear approximation to f(x) = (x+2) at 0 and use it to approximate (2.001)

A: Given :           f(x) = (x + 2)5 at 0 To find :             The linear approximation of f(x)…

Q: Determine k so that f(x, y) = kx(x- y) for 0<x <1,-x< y<x is a joint pdf.

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Q: Find ao of the function f(x) 1-Cosx f(x) =

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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: 24, Find the domain of H function fw =J 2x+3 -1

A: Given,

Q: Suppose f(r) = (In z)e. What is f'(x)?

A: d/dx (f(x)g(x))= f(x)g'(x)+g(x)f'(x)

Q: Prove that is a function f is harmonic =0, then - dx -Ldy =0.

A: Given function f is harmonic such that ∂2f∂x2+∂2f∂y2=0

Q: A function y(t) satisfies th

A: Given, the differential equation                       dydt=-y4-3y3+4y2

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: Find the most general antiderivative of f(x) = -10x – (1 – x²)-1/2, where -1< x < 1.

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Q: Is the function f(z) = (x2 - y2) + 2xyi entire? Why or why not?

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Q: Find f fy. - f(x.y.z) = x - Vy² + 22? + 2z² = (Type an exact answer using

A: Here we have to find fx , fy and fz  of

Q: function, that is 0 everywhere except at t=0, is know as:

A:

Q: Integrate f(x) = 10 ( 1 – x)9 where 1 ≤ x ≤ 3, Using Boole’s rule

A: The function f(x)=101-x9 where 1≤x≤3. We have to integrate this integral using the Boole's Rule.

Q: O De fine fG) in a way that extends g8) = X -3 to be continuows at x=3

A: It is continous function  problem.