What is the limit as x approaches 0 of (x^4+6x)/x ?

The limit as x approaches 0 of (x^4+6x)/x is 6

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limit as x approaches 0 of (x^4+6x)/x

x \to 0 lim (\frac{x ^{4} + 6 x}{x})

6

Solution steps

x \to 0 lim (\frac{x ^{4} + 6 x}{x})

Simplify

\frac{x ^{4} + 6 x}{x} : x^{3} + 6

= x \to 0 lim (x^{3} + 6)

Plug in the value

x = 0

= 0^{3} + 6

Simplify

= 6

x y^{^{'}} - y = x

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\frac{d y}{d x} = \frac{3 y ^{2} + 2 x y}{2 x y + x ^{2}}

\frac{d}{d x} (4 - x^{2} - y^{2})

f (x) = sin (x) + \frac{1}{2} cot (x)

What is the limit as x approaches 0 of (x^4+6x)/x ?
The limit as x approaches 0 of (x^4+6x)/x is 6