What is the limit as x approaches 1 of (2-x)^{4tan(pi/2 x)} ?

The limit as x approaches 1 of (2-x)^{4tan(pi/2 x)} is e^{8/pi}

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limit as x approaches 1 of (2-x)^{4tan(pi/2 x)}

x \to 1 lim ((2 - x)^{4 t a n (\frac{π}{2} x)})

e^{\frac{8}{π}}

Decimal

12.76209 \dots

Solution steps

x \to 1 lim ((2 - x)^{4 t a n (\frac{π}{2} x)})

Apply exponent rules

= x \to 1 lim (e^{4 t a n (\frac{π}{2} x) l n (2 - x)})

Apply the Limit Chain Rule:

e^{\frac{8}{π}}

= e^{\frac{8}{π}}

What is the limit as x approaches 1 of (2-x)^{4tan(pi/2 x)} ?
The limit as x approaches 1 of (2-x)^{4tan(pi/2 x)} is e^{8/pi}