Ufyukyu

This page is only for reference, If you need detailed information, please check here

1 0 $begingroup$ Consider the function $f: (0, infty) to R $ $$ f(x)= begin{cases} int_{x}^{x^2} frac{dt}{log(t)} & xneq 1 \ l & x=1 \ end{cases} $$ Determine $l$ such that the function $f$ should be continuous at 1. For the determined value of $l$ , is the function differentiable? I started out by trying to calculate the following limit, however, I had trouble continuing. $$lim_{xto1}int_{x}^{x^2}frac{mathrm dt}{log(t)}$$ Thank you! real-analysis calculus integration definite-integrals share | cite | improve this question edited Jan 4 at 14:05 math1945 ...

This page is only for reference, If you need detailed information, please check here