What is the limit as x approaches 3 of (tan(x-3))/(3e^{x-3)-x} ?

The limit as x approaches 3 of (tan(x-3))/(3e^{x-3)-x} is 1/2

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limit as x approaches 3 of (tan(x-3))/(3e^{x-3)-x}

x \to 3 lim (\frac{tan ( x - 3 )}{3 e ^{x - 3} - x})

\frac{1}{2}

Decimal Notation

0.5

Solution steps

x \to 3 lim (\frac{tan ( x - 3 )}{3 e ^{x - 3} - x})

Apply L'Hopital's Rule

: x \to 3 lim (\frac{sec ^{2} ( x - 3 )}{3 e ^{x - 3} - 1})

= x \to 3 lim (\frac{sec ^{2} ( x - 3 )}{3 e ^{x - 3} - 1})

Plug in the value

x = 3

= \frac{sec ^{2} ( 3 - 3 )}{3 e ^{3 - 3} - 1}

Simplify

\frac{sec ^{2} ( 3 - 3 )}{3 e ^{3 - 3} - 1} : \frac{1}{2}

= \frac{1}{2}

\frac{1}{x ^{2} + 4}

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\frac{d}{d x} (\frac{tan ( x )}{x ^{2}})

f (x) = \frac{4 x}{x + 3}, (1, 1)

\frac{d}{d θ} (cos (θ) - θ sin (θ))

What is the limit as x approaches 3 of (tan(x-3))/(3e^{x-3)-x} ?
The limit as x approaches 3 of (tan(x-3))/(3e^{x-3)-x} is 1/2