1. Which of the following functions grow faster than e^x as x-> infinity? a) x^4

Question

1. Which of the following functions grow faster than e^x as x-> infinity? a) x^4 b) ln(x) c) e^-x d) 3^x e) 1/2e^x 2.For which pair of functions f(x) and g(x) below, will the lim as x approaches infinity f(x)/g(x) =0 a) f(x)=e^x and g(x)=x^2 b) f(x)=e^x and g(x)=ln(x) c) f(x)=ln(x) and g(x)=e^x d) f(x)=x and g(x)=ln(x) e) f(x)=3^x and g(x)=2^x 3. If f(x)=2x^2+1 then lim x ->0 f(x)-f(0)/x^2 is a) 0 b)1 c)2 d)4 e)nonexistent 4.Which of the following substitutions would help evaluate the integral? Int. sinx/(3+4cosx)^4 dx a) u=3cosx b)u=(3+4cosx)^4 c)u=sinx d)u=(3+4cosx) e)u=tanx/2 5.Find average value of f(x)=e^-x on interval [0,2] a)1-e^2 / 2e^2 b)e^2-1 /2e^2 c)e^-2 -1 d)1-e^2 e) none 1. Which of the following functions grow faster than e^x as x-> infinity? a) x^4 b) ln(x) c) e^-x d) 3^x e) 1/2e^x 2.For which pair of functions f(x) and g(x) below, will the lim as x approaches infinity f(x)/g(x) =0 a) f(x)=e^x and g(x)=x^2 b) f(x)=e^x and g(x)=ln(x) c) f(x)=ln(x) and g(x)=e^x d) f(x)=x and g(x)=ln(x) e) f(x)=3^x and g(x)=2^x 3. If f(x)=2x^2+1 then lim x ->0 f(x)-f(0)/x^2 is a) 0 b)1 c)2 d)4 e)nonexistent 4.Which of the following substitutions would help evaluate the integral? Int. sinx/(3+4cosx)^4 dx a) u=3cosx b)u=(3+4cosx)^4 c)u=sinx d)u=(3+4cosx) e)u=tanx/2 5.Find average value of f(x)=e^-x on interval [0,2] a)1-e^2 / 2e^2 b)e^2-1 /2e^2 c)e^-2 -1 d)1-e^2 e) none

Explanation / Answer

1) d

2) c

3) c

4) d

5) b

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