(a) Prove and verify that if (x) = vx , then f (1) is 8: Vx, then f³(1) is 3/8- (b) Integrate the following functions (1+x²) (i) dx (i) f. (i) (? (x+1)(x² -2,x+2) dx. x2 (c) Integrate the following by substitution of xVI- x² dx. (ii) f cosxsin'x dx. (ii) f, 5xv2x² + 7 dx

Q: --1/0 -1 -1 1,0

A: As we can see  in the figure the tangent line passes through the point x=2. Slope of tangent line…

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A: Given, y=f(x)=2x3+6x2-5x+1 In this we have to find differentiation of function till when all the…

Q: Consider the function y = (a) Find the x- and y-intercepts of f(x)

A: An x-intercept of a function f(x) is a point on the x-axis at which the graph of the function f(x)…

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Q: Let f (x) = Evaluate the following. Simplify if possible. 9x +7 f (x) – f(a) a) 7 where A = A' for x…

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Q: The point (-2,1) is in the domain of the function given by f(x,y) = sqrt(x+2y) + ln(x+3y) True or…

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Q: The linearization of f (x) = x² based at 3 is L (x) = [ Select ] [ Select ] (x - [ Select ] Done […

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Q: Let f(x) = v9x+ 8 and g(x) = x+9 be functions from R to R. Find the following. a) (f • g)(x) = %3D…

A: We are given f(x)=9x+8 and g(x)=x+9 and we need to find different composition of the function.

Q: Let f(x, y) = 2x - 4y + 7. Find the following. (a) f(3,-1) (b) f(-5, 1) (c) f(-5, -4) (d) f(0, 7)

A: Since you have posted multiple subparts, as per our policy we will answer first three subparts.…

Q: f(x) = x+ 4/x

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Q: Approximate f(3) centered at 0 of f(x) = 2x³ + 3x² + x - 1. %3D

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Q: Find the inverse function to y=F(x)=5sqrt(x+3) X=G(y)=

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Q: The vertex of the parabola f(x) =(x+3) - 4 is а) (-3, -4) b) (3, -4) с) (3, 4) d) (-3, 4)

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Q: 1 f (x) =

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Q: e) k(x) = (2x-1) ³x

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Q: Let f(x)= ax'+x² + bx +6 where a and b are real numbers, and f(2)=3. Find the value of f(-2).

A: f(-2) = 17  The detailed solution is as follows below:

Q: F = (2+-1) dt

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Q: Find f(x) if f (x) = x/x given f(1) = 2. %3D

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Q: Find y as a function of a if y(0) = 8, 3/(0) = 8, "(0) = 25, "(0) = 0. y(x) = || (4) 10y" +25y"=0, 1

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Q: Differentiate the functions. a) f(x) = 2 – 5x + b) f(x) = e* + sinx c) f(x) =

A: Differentiate wrt x

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Q: 2x-3 Let f(x)= Compute (1 -i/2). (1 – i/2)=

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Q: Differentiate the following function. 6x2 +5 y = x2 +1 dx (x² + 1)< dy (x² + 1) • : (6x² + 5) + (6x²…

A: You just need to apply quotient formula in order to solve this.

Q: For the function f(z) 2(x – 5) + 7, which of these equations describes f '(r), the inverse of the…

A: We wil use concept of inverse function to find the answer.

Q: Let n be a positive integer. Define the function fn(z) by dzn (2²+2x+2)". Find the value of fn(-1 +…

A: Solution:Given: Let be a positive integer. the function is defined bywe have to find the value of

Q: If f(2) = (3z)²a² z+2/a find and simplify f(/@). %3D

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Q: 2. (a) (5 points) Let f(x) = Vr +1 and g(x) = x² + 2x. Find (f o g)(1) and (go f)(1). %3D %3D 1+ x…

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Q: Express the function in the form fog. (i) F(x) = (2r + r*)ª. (ii) F(r) = %3D 1+ VE

A: Answer

Q: Determine f'(x)given f(x) =(3x – 6) • Vx

A: We are given a function which is product of two different functions i.e. f(x)=(3x-6).3√x we need to…

Q: Can f(z) = | Re (z2) | + i.Im (-z) be derived from the function z=0? Show it.

A: