Question

Use the Comparison Theorem to determine whether the integral is convergent or divergent.

Answer 1

\[\int\limits_{0}^{1}{(\sec x)^{2}\over x \times \sqrt x}dx\]

Answer 2

i am thinking you can get rid of the secant

Answer 3

on the interval (0,1), \(sec(x)=\frac{1}{\cos(x)}\) is largest at 0 (where it is 1) and smallest at 1

Answer 4

so you have \[\int_0^1\frac{1}{\cos^2(x)x^{\frac{3}{2}}}\]

Answer 5

The integral
\[\int_0^1 \frac {dx} { x^{3/2}}
\]
is divergent.

Answer 6

think this does not converge, since your problem is at x = 0 and
\[\int\frac{dx}{x^{\frac{3}{2}}}\] is divergent