# How do you test the improper integral #int sintheta/cos^2theta# from #[0,pi/2]# and evaluate if possible?

To test the improper integral (\int_0^{\frac{\pi}{2}} \frac{\sin(\theta)}{\cos^2(\theta)} , d\theta), use the substitution (u = \cos(\theta)) to transform the integral into a standard form. Then, evaluate it over the appropriate range. This integral diverges.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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