Let > 0 and 6 > 0 be real numbers that satisfy e' (1+a+²) = eª (1+b+ 2 ) eb Prove or disprove that a = b must hold.

Q: sinx If Ax) = 2**, find f'(0). A 2 cln2 D1

A:

Q: Suppose that f has an inverse and f(4) = –1, f'(4) : If 11 금 what is g'(-1)?

A: Given, f(4)=-1, f'(4)=4/11

Q: Suppose that f'(x) = 2x for all x. a) Find f(4) if f(0) = 0. b) Find f(4) if f(2)= -1. c) Find f(4)…

A: Given f'( x ) = 2x

Q: 4 Suppose that f'(x) = 2x for all x a) Find f(5) if f(0) = 0. b) Find f(5) if f(4) = 14. c) Find…

A:

Q: Suppose X,~ Uniform(0, 2) and X, ~ Uniform(0, X,). Find E[2X,+X,].

A: Given,X1 ~U(0,2)X2 ~U(0,X1)E(X1)=2+02=1E(X2)=X1+02=X12

Q: a) x³ - x f (x) = 2x² + x − 1 - b) f(x) = ax + b cx - d

A: Here we have to evaluate for a) and b) the value of f'(x).

Q: 3 Let f(x)= x³ - 2x+: Calculate by definition f'(1). X

A: given function to find the derivative

Q: Find numbers a and b so that f'(1) exists for ax² + b 1 x² f(x) = if if x 1.

A:

Q: 8. Find all the roots of f(x) =x* - 4x' + 6x² – 4x+5 if 2-iis one root.

A: Topic- roots of polynomial

Q: Let 11 f(x) = ( – 2a² – 4)(7z² – 4)" - - f'(x) =

A:

Q: Suppose that f'(x) = 2x for all x. a) Find f(1) if f(0) = 0. b) Find f(1) if f(2)=0. c) Find f(1) if…

A: Given that f'(x)=2x for all x. We have to find the required values.

Q: 3x'e* (x* +1)* 3e a) -+C 2(x² +1) 3e* b) 2(x² +1) +C x? +3 x +1 3 c) +C .2

A:

Q: 7 f(x) = 2x' + х— 2 + f'(x) = 2.

A:

Q: 22. Find f/(x) and simplify 1 -1 a) f(z) 3-52+1 3 b) f(x) 1.8Vc) f(x) = 32

A: Given, functions