Expert Answer to "Find the limits. limx→−∞2x+4x5x−2x"

naivlingr

Answered question

2020-12-21

Find the limits.

lim_{x \to - \infty} \frac{2^{x} + 4^{x}}{5^{x} - 2^{x}}

krolaniaN

Skilled2020-12-22Added 86 answers

Consider the limit

lim_{x \to - \infty} \frac{2^{x} + 4^{x}}{5^{x} - 2^{x}}

Solve:

lim_{x \to - \infty} \frac{2^{x} + 4^{x}}{5^{x} - 2^{x}}

Take

2^{x}

common from numerator and denominator

= lim_{x \to - \infty} \frac{2^{x} (1 + \frac{4^{x}}{2^{x}})}{2^{x} (\frac{5^{x}}{2^{x}} - 1)}

= lim_{x \to - \infty} \frac{2^{x} (1 + (\frac{4}{2})^{x})}{2^{x} ((\frac{5}{2})^{x} - 1)}

= lim_{x \to - \infty} \frac{(1 + 2^{x})}{((2.5)^{x} - 1)}

= \frac{lim_{x \to - \infty} (1 + 2^{x})}{lim_{x \to - \infty} ((2.5)^{x} - 1)}

= \frac{(1 + 2^{- \infty})}{({2.5}^{- \infty} - 1)}

= \frac{(1 + 0)}{(0 - 1)}

= - 1

Answer: -1

Jeffrey Jordon

Expert2022-04-01Added 2605 answers

Answer is given below (on video)

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