What is the limit as x approaches 0 of (1+x^2)^{x-2} ?

The limit as x approaches 0 of (1+x^2)^{x-2} is 1

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limit as x approaches 0 of (1+x^2)^{x-2}

x \to 0 lim ((1 + x^{2})^{x - 2})

1

Solution steps

x \to 0 lim ((1 + x^{2})^{x - 2})

Plug in the value

x = 0

= (1 + 0^{2})^{0 - 2}

Simplify

= 1

x \to 0 lim (1 + 6 x)

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

x \to (0) lim (\frac{x - y}{x + y})

x \to 0 + lim (sin^{x} (\frac{1}{x}))

θ \to 0 lim (cos (θ))

What is the limit as x approaches 0 of (1+x^2)^{x-2} ?
The limit as x approaches 0 of (1+x^2)^{x-2} is 1