(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: Find the inverse of the following functions (a) f :R +R, f(x) = 2, (b) f:R- {}→R - {}, f(x) = - 3-2z…

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Q: Express f(z) = x-1-iy (x−1)² + y² in terms of z.

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Q: F(x)= 7/(x+9) find the inverse

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Q: 1. Find the most general antiderivative or indefinite integral for the function. (Ilint: Using a…

A: to find integration.

Q: Find the linearization L(x) of the function f(x)=x to the 4th power +2x to the 2nd power +1 at x=2.…

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Q: -4x For the function f(x) = e¯X+4e*, then f(x) = %3D

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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: of Find (7,- 2) if f(x,y) = 4x² + 7xy - 3y? + 6x - 5y - 2. of (7,- 2) = (Simplify your answer.)

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Q: Find y as a function of x if x²y" +5xy - 12y = x², y(1) = −9, y(1) = 9. y=

A: We have to find as a function of .

Q: Find the inverse Laplace transform ƒ(t) = L−¹ {F(s)} of the function F(s) = s² = s-1 8s + 17

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Q: Find f′(x), if f(x)=(x4+1)(3x−1).

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Q: If y = g(u) = u2 / (1-2u) and u = h(x) = x +5, determine the composite functions  (a). g(h(x))…

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Q: Let a, b 0. Find f(100) (a) provided that x³ (a - bx)²* f(x) =

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Q: Which of the following is the sum of the series 00 3 3 (n+1)2 n-1 Select one: O A. 3/4 O B. 1/3 O…

A: Given series, ∑n=1∞3n2-3n+12

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: Find f′(0), where f(x)= (x|x|)/(2+⌊x⌋)

A: Consider the given function fx=xx2+x

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: If f(t) = (t2 + 1)(2t - 3et), determine the first derivative of f(t). a. (t2 + 1)(2 - 3et) + (4t2 -…

A: Given function for derivative f( t ) = ( t2 + 1 )( 2t - 3et )Formula used ddx( u.v ) = udvdx +…

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

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