lim x → ∞ ( 2 + x ) 40 ( 4 + x ) 5 ( 2 − x ) 45 Options: A . &nbsp − 1 B . &nbsp 1 C . &nbsp 16 D . &nbsp 32

Answer: Option A : A lim x → ∞ ( 2 + x ) 40 ( 4 + x ) 5 ( 2 − x ) 45 = lim x → ∞ x 45 ( 2 x + 1 ) 40 ( 4 x + 1 ) 5 x 45 ( 2 x − 1 ) 45 = ( 1 ) 40 ( 1 ) 5 ( − 1 ) 45 = ( 1 ) 45 ( − 1 ) 45 = − 1

limx→∞(2+x)40(4+x)5(2−x)45

Discussion Forum : Limits Continuity And Differentiability

Question -

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

Options:

A .

- 1

B .

1

C .

16

D .

32

Answer: Option A
:
A

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}}

= \frac{(1)^{45}}{(- 1)^{45}}

= - 1

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