26. Let f (x) = vx - 1 and g(x) = x² – 4. A. Find (fog)(x) and (gof)(x). B. Find all real values of x for which (fog)(x) = (gof)(x).

Q: Let c>0 be a constant.  Is this result true or false?

A:

Q: Suppose that g is a continuous function. Find the general solution of y" – y = g(t).

A:

Q: is The antiderivative of the function f(x) =. 2x а. 2 In x + c b. 1

A: Givenf(x)=12xAntiderivative of f(x)=?Antiderivative is nothing but integral.

Q: 5. Show that the function h(x, y) defined by if r2 + y? 1 is discontinuous.

A:

Q: (b) f(x) = where A; E S™ – (det(Ao + x1A1 + ...+ xn An))/m, on {x | Ao + ¤1A1 ++xnAn > ► 0},

A:

Q: 出w-2 Verify that Wメy Wyx for the functions's T- f(xsy) = En (2X +34) fcxyy) = e+x Luy +y Lnx 2-

A: Since you have posted multiple question at a time as per guidelines we can solve only one question…

Q: Find and classify all the critical points of the following function: F(x,y)=(3x +4x')( y²+2y)

A: We need to find critical point and classify them.

Q: Find the general antiderivative of f(x) = + C - 5x¹ x² +6√x

A:

Q: 2. Find and classify the critical points of the function f (x, y) = 6x2 – 2x³ + 3y? + 6xy

A: The solution is given below in the next step:

Q: 8. Find the antiderivative of the following functions: a) f (x) = 3 b) f (x) = 2x c) f (x) = 5x

A: We have given to find derivative of the function  a) f(x) = 3  f'x = ddxfx f'x=ddx3 f'x=0 b) f(x) =…

Q: Suppose that f(x) is an antiderivative of f(x) = V1 + xt. Express JoV1 + x* dx in terms of F and…

A:

Q: Let g=yf(xy). Show that: - дд у ду дд - Х = g дх -

A:

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

A:

Q: If L(x)=mx+b is the linearization of f(x) 2x-x +3 at x-1, then m3 Using L to approximate 2(1.01)…

A:

Q: If f (x, y) = Vr³ + y³ In(x² + y²)e*in (zy+y') + x³y+ 10 , then f. (1,0) =

A: A scalar function f(x,y) is a rule that is used to associate a number or quantity with a particular…

Q: 25. For y = f(x) = x2 - 3, x = 5, and Ax = 0.1, find Ay and f'(x) Ax. %3D

A: Given: fx=x2-3 ,x=5 and ∆x=0.1

Q: For what value of b is

A:

Q: Find the antiderivative F(x) of f(x)= 3√x that satisfies F(1)=2

A: The given function, f(x)=x3

Q: Find the value of c which satisfies the conclusion of Rolle's Theorem with the given f (x) =x- 3x,…

A:

Q: 7. Let f(x, y) = 10xy* + x°y². Find fyyy. 4

A:

Q: {(u)= (u² -3)*

A: Given the function is  f(u) = 12u2-32. We have to find f'(u).

Q: 6) If y=x² +1+ f dt , prove that y"= 2 - x2

A:

Q: Differentiate f(x) = f'(x) = 2 ax with respect to x. Assume that a and k are positive constants. k+x

A: To differentiate fx=ax2k+x with respect to x. Assume that a and k are positive constants.

Q: Show that f(x1, x2) = 2 - (x1 - 1)^2 - e^x2^2 is concave.

A: the given function is fx1,x2=2-x1-12-ex22 To find the function is concave we have to show all its…

Q: of of and ду For the function f(x,y) = In (7x + 9y), find

A: The given function,     f(x,y)=ln7x+9y

Q: Find the linearization L(x) of f(x) at x=a. f(x)=x/2x+9 a=0

A:

Q: what is the antiderivative F(x) of f(X) = 3x1/2-x-1 that satisfies the condition  F(4)= 0? A,…

A: The given function is fx=3x12-x-1 that satisfies the condition F4=0. Find the antiderivative of Fx.

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

A: Introduction :

Q: Let Find fa, fay and fryz f(x, y) =In(xy)-26x¹0 y 10

A:

Q: Let f(x)=6x2+1f(x)=6x2+1.Enter an antiderivative of f(x) . . .

A: The given function is,

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

A: Given,

Q: The antiderivative of the function 4 + 10x is. x2 f(æ) = 4 + 5.0x2 + c - -4 5.0x2 + c -10 + 2.0x2 +…

A:

Q: 2. Find and classify all the extrema of the function f (x, y) = 4xye e-(x²+y²)/4

A: The given function is:  f(x,y) = 4xy e-(x^2 +y^2)/4

Q: Let f(x) = ax* + bx . If (1,6) is a relative extremum point, then b is?

A:

Q: Let f(x,y)=2x²+y²-8x-6y+12. 1- Find Vf at (1,1). 2-Find the extreme values of f.

A: Given data: The expression for the given function is f(x,y)=2x2+y2-8x-6y+12. 1) The given point  is…

Q: Consider the function f(x) = 7x° + 9x° – 9 - 9. Enter the antiderivative of f(x) + C

A: T

Q: Find the linearization of L(x) of f(x) at x=a f(x)=StartRoot x2 +17, End Root a =8

A: Given function and point is

Q: 2. Consider the three functions below: S(z) = 2z S(z) =r S(x) = 2"

A: fx=2x,fx=x2 and fx=2x (a) Take the value of x as -2,-1,0,1,2,3. x fx=2x fx=x2 fx=2x -2 -4 4 14…

Q: Compute the linearisation l(x) of f(x) = √1+x3 at x=2 and use this to estimate f(2.05)

A: Given function is: fx=1+x3 At x0=2 So the linear approximation is: Lx≈fx0+f'x0x-x0…

Q: Find the general antiderivative, F(x), of the function f(x) = 2x -6x² +x+ 2.

A: we will answer the first question since exact one was not specified. Please resubmit the question…

Q: Consider the following function: f(r) = 2r + 3z² – 12z Find the critical numbers of f. (x = ?)

A:

Q: 4. Find the linearization L of the function f(x)=Vx+3 at a = 1 and use it to approximate f(x) =…

A:

Q: 6) Show that TE[f (t - a)] = e-i2mva TF[f(t)] where a e R".

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

Q: 4. Let F : R² → R² defined by F(x,y) = (2x +3y, –x +y). Is F a linear? Why?

A: Given

Q: 2R then the constants R TCX If f(x) Rsin .2 S,f' and f(x)dx and S are respectively.

A: Introduction :Here we have asked to find the value of R and S

Q: Let a +b = 4, where a 0 for all x, prove that g(x) dr + g(x) dx increases as (b- a) increases.

A:

Q: 3 The antiderivative of the function f(x) = + 9x is x2 -3 4.5x2 + c 3 + 18.0a? + c 6- + 1.5x + c 3 +…

A:

Q: b) Let X₁, X₂, Xn-f(x) = {0x-(0*) x>1 e. w. find Suff. Comp. St.

A: Given that