Lim_x→∞(2+x)^40(4+x)^5(2 x)^45 =lim_x→∞x^45(2x+1 )^40(4x+1 )^5x^45(2x 1 )^45 =(1)^40(1)^5( 1)^45= 1 nbsp; ...

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Indeterminate Forms

limx→∞2+x404+...

Question

$lim x \to \infty \frac{(2 + x)^{40} (4 + x)^{5}}{(2 - x)^{45}}$

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Solution

The correct option is A $- 1$
$lim x \to \infty \frac{(2 + x)^{40} (4 + x)^{5}}{(2 - x)^{45}} = lim x \to \infty \frac{x^{45} {(\frac{2}{x} + 1)}^{40} {(\frac{4}{x} + 1)}^{5}}{x^{45} {(\frac{2}{x} - 1)}^{45}} = \frac{(1)^{40} (1)^{5}}{(- 1)^{45}} = - 1$

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