What is the limit as x approaches infinity of (u(x)k+1)/(u(x)k) ?

The limit as x approaches infinity of (u(x)k+1)/(u(x)k) is Undefined

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limit as x approaches infinity of (u(x)k+1)/(u(x)k)

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

Undefined

Solution steps

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

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

= \frac{1}{k} \cdot x \to \infty lim (\frac{u ( x ) k + 1}{u ( 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{1}{k} \cdot \frac{lim _{x \to \infty} ( u ( x ) k + 1 )}{lim _{x \to \infty} ( u ( x ) )}

x \to \infty lim (u (x) k + 1) = \infty

x \to \infty lim (u (x)) = u (\infty)

= \frac{1}{k} \cdot \frac{\infty}{u \cdot \infty}

Simplify

\frac{1}{k} \cdot \frac{\infty}{u \cdot \infty} :

Undefined

= Undefined

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x \to 4 lim (\frac{2 - 7 x}{4 - x})

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

x \to - 4 lim (\frac{5 x}{∣ x + 4 ∣})

x \to 0 lim ((- 4 ln (x))^{x})

What is the limit as x approaches infinity of (u(x)k+1)/(u(x)k) ?
The limit as x approaches infinity of (u(x)k+1)/(u(x)k) is Undefined