What is the limit as x approaches infinity of 2/(3+4^{1/x)} ?

The limit as x approaches infinity of 2/(3+4^{1/x)} is 1/2

Popular >

limit as x approaches infinity of 2/(3+4^{1/x)}

x \to \infty lim (\frac{2}{3 + 4 ^{\frac{1}{x}}})

\frac{1}{2}

Decimal

0.5

Solution steps

x \to \infty lim (\frac{2}{3 + 4 ^{\frac{1}{x}}})

x \to a lim [c \cdot f (x)] = c \cdot x \to a lim f (x)

= 2 \cdot x \to \infty lim (\frac{1}{3 + 4 ^{\frac{1}{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

= 2 \cdot \frac{lim _{x \to \infty} ( 1 )}{lim _{x \to \infty} ( 3 + 4 ^{\frac{1}{x}} )}

x \to \infty lim (1) = 1

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

= 2 \cdot \frac{1}{4}

Simplify

2 \cdot \frac{1}{4} : \frac{1}{2}

= \frac{1}{2}

x \to \infty lim (- 7 x - 4)

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

x \to 0 lim (\frac{1 - cos ( 7 x )}{1 - cos ( 3 x )})

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

x \to - 1 lim (ln ∣ 1 + x ∣)

What is the limit as x approaches infinity of 2/(3+4^{1/x)} ?
The limit as x approaches infinity of 2/(3+4^{1/x)} is 1/2