(Solved): (a) Use the Maclaurin series (same as Taylor series centered at 0 ) to evaluate the following limit ...

(a) Use the Maclaurin series (same as Taylor series centered at 0 ) to evaluate the following limit \[ \lim _{x \rightarrow 0} \frac{x-\ln (1+x)}{x^{2}} . \] (b) Evaluate the indefinite integral as an infinite series \[ \int \frac{\cos \left(x^{2}\right)-1}{x^{2}} d x . \]