# Tagged Questions

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### Evaluating integral limit in two ways gives different limits

Problem Show that $$\lim\limits_{h \rightarrow 0^{+}} \int_{-1}^{1} \frac{h}{h^{2}+x^{2}} \, dx = \pi.$$ I can do this by evaluating the integral directly and showing that it is equal to ...
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### Recommended Textbook/Resources

I'm looking for a textbook or resources my younger brother could use. (He is in year 9, equivalent to US high school freshman) He is wanting to advance upon his math, he currently does exercises out ...
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### Sequence of learning mathematics from basic algebra to calculus.

What would be a step by step sequence of learning mathematics from basic algebra to basic calculus? I pose this question because I am in the process of self-learning mathematics as a preparation for a ...
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### Definition of limit of function

I'm reading Calculus: Basic Concepts for High School Students and am trying to digest the definition of 'limit of function'. There are two details that I am struggling to fully accept: If you are ...
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### Using Picard-Lindelöf Theorem to elegantly demonstrate uniqueness of an IVP

I am trying to keep this question clean and short, therefore I won't write down the entire theorem of Picard-Lindelöf here. Problem: $$y'=1+y^2 =:F(y), \ y(0)=0$$ Find a solution on a ...
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### Reference for power series

I would need some references for power series, Taylors series of elementary functions, derivation and integration of power series, convergence of sequences of functions and series of functions. The ...
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### Calculating mean vector of a multivariate distribution

I have a question concerning calculating the mean vector (vector of expected values) of a general multivariate distribution. I try to obtain the mean vector by doing a vector integration and I ...