What is the limit as x approaches 0 of (1+4x)^{-3/x} ?

The limit as x approaches 0 of (1+4x)^{-3/x} is 1/(e^{12)}

Popular >

limit as x approaches 0 of (1+4x)^{-3/x}

x \to 0 lim ((1 + 4 x)^{- \frac{3}{x}})

\frac{1}{e ^{12}}

Decimal Notation

6.14421 E - 6

Solution steps

x \to 0 lim ((1 + 4 x)^{- \frac{3}{x}})

Simplify

(1 + 4 x)^{- \frac{3}{x}} : \frac{1}{( 1 + 4 x ) ^{\frac{3}{x}}}

= x \to 0 lim (\frac{1}{( 1 + 4 x ) ^{\frac{3}{x}}})

x \to a lim [\frac{f ( x )}{g ( x )}] = \frac{lim _{x \to a} f ( x )}{lim _{x \to a} g ( x )}, x \to a lim g (x) \neq = 0

With the exception of indeterminate form

= \frac{lim _{x \to 0} ( 1 )}{lim _{x \to 0} ( ( 1 + 4 x ) ^{\frac{3}{x}} )}

x \to 0 lim (1) = 1

x \to 0 lim ((1 + 4 x)^{\frac{3}{x}}) = e^{12}

= \frac{1}{e ^{12}}

x \to - \infty lim (x + 3)

x \to 0 lim (1^{\frac{l n ( 6 )}{x}})

x \to - 4 lim (∣ x + 4 ∣ - 2 x)

x \to 0 lim (\frac{( 4 x ^{2} )}{e ^{4 x} - 4 x - 1})

x \to 2 lim (\frac{3 x}{x ^{2} - 4})

What is the limit as x approaches 0 of (1+4x)^{-3/x} ?
The limit as x approaches 0 of (1+4x)^{-3/x} is 1/(e^{12)}