What is the limit as x approaches-1 of (sin(pi/2)x+2^{-3x})^2 ?

The limit as x approaches-1 of (sin(pi/2)x+2^{-3x})^2 is 49

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limit as x approaches-1 of (sin(pi/2)x+2^{-3x})^2

x \to - 1 lim ((sin (\frac{π}{2}) x + 2^{- 3 x})^{2})

49

Solution steps

x \to - 1 lim ((sin (\frac{π}{2}) x + 2^{- 3 x})^{2})

Plug in the value

x = - 1

= (sin (\frac{π}{2}) (- 1) + 2^{- 3 (- 1)})^{2}

Simplify

(sin (\frac{π}{2}) (- 1) + 2^{- 3 (- 1)})^{2} : 49

= 49

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What is the limit as x approaches-1 of (sin(pi/2)x+2^{-3x})^2 ?
The limit as x approaches-1 of (sin(pi/2)x+2^{-3x})^2 is 49