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

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

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

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

diverges

Solution steps

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

x \to a - lim f (x) \neq = x \to a + lim f (x)

then the limit does not exist

x \to 0 + lim ((1 + 2 x)^{\frac{1}{2 x ^{2}}}) = \infty

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

= diverges

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