What is the limit as x approaches 0 of (4x-x^2)/x ?

The limit as x approaches 0 of (4x-x^2)/x is 4

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limit as x approaches 0 of (4x-x^2)/x

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

4

Solution steps

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

Simplify

\frac{4 x - x ^{2}}{x} : 4 - x

= x \to 0 lim (4 - x)

Plug in the value

x = 0

= 4 - 0

Simplify

= 4

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

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

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

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

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

What is the limit as x approaches 0 of (4x-x^2)/x ?
The limit as x approaches 0 of (4x-x^2)/x is 4