Question

1a) Evaluate the limit as x goes to infinity using l'hopitals rule

(x^-1/3)/sin(1/x)

1b) Evaluate the improper integral (if convergent find it's value)

(secx-tanx)dx where a= 0 and b=pi/2

Answer 1

(A)

we can plug x=inf

so, we can use L'hospital rule

we can find derivative of top and derivative of bottom

we can simplify it

now, we can plug x=inf

............Answer

(B)

we can set up integral

Firstly, we can find antiderivative

now, we can plug bounds

and we get

............Answer