# Textbooks for real analysis that will help me solve actual problems??

Are there any analysis textbooks with concrete examples and problem sets?

I've studied mathematical analysis and real analysis with Rudin.

There was not much trouble for me in understanding what was written inside those textbooks. But recently I've found I have a problem while preparing for my GRE maths test. I know all the definitions and theorems in the textbooks but I'm not really able to apply them to real questions.

So for instance I know what a limit is and what traits it has, but if you give me a complicated function and ask me to find the limit I'm not really able to do so. I think maybe this is because abstract theory and application are slightly different and even if I know the theory I need some practice in application to solve problems for my GRE test.

And I don't think Rudin will be the one who can help. So do any of you know good textbooks that will help me prepare in learning the 'practical' maths?

• It is surprising to me if you are talking about solving $\frac{0}{0}$ and $\frac{\infty}{\infty}$ type problems, part of high school lore while Rudin is university lore. The essential idea is that the numerator must balance the denominator in a limiting sense as $\frac{0}{0}$ is uncomputable. So you simplify the expressions in numerator & denominator & cancel out whatever is making the expressions $0$. – Ricky Aug 21 '16 at 16:56
• @Ricky: can you quote the sentence where the OP refers to "solving $\frac{0}{0}$ and $\frac{\infty}{\infty}$ type problems"? – symplectomorphic Aug 21 '16 at 18:03
• @symplectomorphic: I don't know what is so tough then after mastering Rudin. – Ricky Aug 21 '16 at 18:20
• @symplectomorphic: Also, the definition of derivative i.e. $\frac{dy}{dx} = \lim_{\delta x \rightarrow 0}\frac{\delta y}{\delta x}$ is nothing but a $\frac{0}{0}$ problem. – Ricky Aug 21 '16 at 18:30