Question-140384

Question Number 140384 by Willson last updated on 07/May/21

Answered by benjo_mathlover last updated on 07/May/21

(2) \lim_{x \to 0} \frac{{(x^{p} + 1)}^{n} {(x^{q} + 1)}^{m} - 1}{x} =

\lim_{x \to 0} \frac{(1 + {nx}^{p}) (1 + {mx}^{q}) - 1}{x} =

\lim_{x \to 0} \frac{1 + {mx}^{q} + {nx}^{p} + {mnx}^{p + q} - 1}{x} =

\lim_{x \to 0} \frac{{mx}^{q} + {nx}^{p} + {mnx}^{p + q}}{x} =

\lim_{x \to 0} {mx}^{q - 1} + {nx}^{p - 1} + {mnx}^{p + q - 1} = 0