What is the limit as x approaches 0 of (sec(x))^{4x} ?

The limit as x approaches 0 of (sec(x))^{4x} is 1

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limit as x approaches 0 of (sec(x))^{4x}

x \to 0 lim ((sec (x))^{4 x})

1

Solution steps

x \to 0 lim ((sec (x))^{4 x})

Plug in the value

x = 0

= (sec (0))^{4 \cdot 0}

Simplify

sec^{4 \cdot 0} (0) : 1

= 1

x \to 0 + lim (- \frac{sin ( x )}{2 \cdot x})

x \to 1 lim (\frac{x - x ^{4}}{1 - x})

x \to \infty lim (\frac{1 + x}{3 1 + x})

x \to \infty lim (\frac{e ^{5 x}}{3 - e ^{2 x}})

x \to 0 lim (x cos (2 x))

What is the limit as x approaches 0 of (sec(x))^{4x} ?
The limit as x approaches 0 of (sec(x))^{4x} is 1