What is the limit as x approaches 0 of (3^{x^2}-1)/x ?

The limit as x approaches 0 of (3^{x^2}-1)/x is 0

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limit as x approaches 0 of (3^{x^2}-1)/x

x \to 0 lim (\frac{3 ^{x^{2}} - 1}{x})

0

Solution steps

x \to 0 lim (\frac{3 ^{x^{2}} - 1}{x})

Apply L'Hopital's Rule

: x \to 0 lim (\frac{2 ln ( 3 ) \cdot 3 ^{x^{2}} x}{1})

= x \to 0 lim (\frac{2 ln ( 3 ) \cdot 3 ^{x^{2}} x}{1})

Plug in the value

x = 0

= \frac{2 ln ( 3 ) \cdot 3 ^{0^{2}} \cdot 0}{1}

Simplify

\frac{2 ln ( 3 ) \cdot 3 ^{0^{2}} \cdot 0}{1} : 0

= 0

\frac{1}{x + 6}

\int (- 2 x + 3) d x

3 x^{2} + 8

\int \frac{1}{v ^{2} - v} d v

f (θ) = 3 sin (θ)

What is the limit as x approaches 0 of (3^{x^2}-1)/x ?
The limit as x approaches 0 of (3^{x^2}-1)/x is 0