What-is-the-F-0-so-that-the-function-F-x-4-x-1-3-sin-x-4-ln-1-x-2-3-becomes-continous-at-x-0-

Question Number 129072 by liberty last updated on 12/Jan/21

What is the F (0) so that the function

F (x) = \frac{{(4^{x} - 1)}^{3}}{\sin (\frac{x}{4}) \ln (1 + \frac{x^{2}}{3})} becomes continous

at x = 0 ?

Answered by MJS_new last updated on 12/Jan/21

l^{'} Hopital 3 times gives

\lim_{x \to 0} F (x) = 96 {(\ln 2)}^{3}

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