What is the limit as x approaches 0 of (6e^x-6)/x ?

The limit as x approaches 0 of (6e^x-6)/x is 6

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limit as x approaches 0 of (6e^x-6)/x

x \to 0 lim (\frac{6 e ^{x} - 6}{x})

6

Solution steps

x \to 0 lim (\frac{6 e ^{x} - 6}{x})

Apply L'Hopital's Rule

: x \to 0 lim (\frac{6 e ^{x}}{1})

= x \to 0 lim (\frac{6 e ^{x}}{1})

Plug in the value

x = 0

= \frac{6 e ^{0}}{1}

Simplify

= 6

\frac{d y}{d x} = \frac{( x ^{2} y - y )}{( y + 1 )}

\frac{d}{d x} (cos (4 x) + sin (4 x))

10 y^{^{''}} + 1000 y = 0

\frac{\partial}{\partial u} (2 sin (u) cos (v))

y = 4 (x + 1), y = 5 (x + 1), x = 7

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