What is the limit as x approaches 0 of (x^2+6x)/x ?

The limit as x approaches 0 of (x^2+6x)/x is 6

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limit as x approaches 0 of (x^2+6x)/x

x \to 0 lim (\frac{x ^{2} + 6 x}{x})

6

Solution steps

x \to 0 lim (\frac{x ^{2} + 6 x}{x})

Simplify

\frac{x ^{2} + 6 x}{x} : x + 6

= x \to 0 lim (x + 6)

Plug in the value

x = 0

= 0 + 6

Simplify

= 6

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

x \to \frac{1}{2} lim (\frac{5}{4})

x \to 1 + lim (1 - x)

x \to - 5 - lim (\frac{- 3 x}{x + 5})

h \to 0 lim (\frac{cos ( \frac{3 π}{2} + h ) - cos ( \frac{3 π}{2} )}{h})

What is the limit as x approaches 0 of (x^2+6x)/x ?
The limit as x approaches 0 of (x^2+6x)/x is 6