What is the limit as x approaches infinity of (2-x)/(x+1)+(2^{-x}*x)/(x+2) ?

The limit as x approaches infinity of (2-x)/(x+1)+(2^{-x}*x)/(x+2) is -1

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limit as x approaches infinity of (2-x)/(x+1)+(2^{-x}*x)/(x+2)

x \to \infty lim (\frac{2 - x}{x + 1} + \frac{2 ^{- x} \cdot x}{x + 2})

- 1

Solution steps

x \to \infty lim (\frac{2 - x}{x + 1} + \frac{2 ^{- x} x}{x + 2})

x \to a lim [f (x) \pm g (x)] = x \to a lim f (x) \pm x \to a lim g (x)

With the exception of indeterminate form

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

x \to \infty lim (\frac{2 - x}{x + 1}) = - 1

x \to \infty lim (\frac{2 ^{- x} x}{x + 2}) = 0

= - 1 + 0

Simplify

= - 1

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What is the limit as x approaches infinity of (2-x)/(x+1)+(2^{-x}*x)/(x+2) ?
The limit as x approaches infinity of (2-x)/(x+1)+(2^{-x}*x)/(x+2) is -1