Better Students Ask More Questions.
Calculate lim F(x) given F(x)=integral (1<x)f (t)dt f(x)=1/(2-sin x)
1 Answer | add yours
You need to use the following definition of sine function, such that:
`sin x < 1 => -sin x < 1`
Adding 2 both sides of inequality, yields:
`2 - sin x < 2 + 1 => 2 - sin x < 3 => 1/(2 - sin x) > 1/3 => f(x) > 1/3`
Integrating both sides the inequality `1/(2 - sin x) > 1/3` yields:
`int 1/(2 - sin x) dx > int (dx)/3 = x/3`
Evaluating the limit yields:
`lim_(x->oo) int 1/(2 - sin x) dx > lim_(x->oo) x/3 = oo`
Hence, evaluating the limit `lim_(x->oo) F(x) = lim_(x->oo) int 1/(2 - sin x) dx = oo` .
Posted by sciencesolve on June 26, 2013 at 5:43 PM (Answer #1)
Join to answer this question
Join a community of thousands of dedicated teachers and students.