What is the limit as x approaches 1 of (x+1)/(sqrt(6x^2+3)+3x) ?

The limit as x approaches 1 of (x+1)/(sqrt(6x^2+3)+3x) is 1/3

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limit as x approaches 1 of (x+1)/(sqrt(6x^2+3)+3x)

x \to 1 lim (\frac{x + 1}{6 x ^{2} + 3 + 3 x})

\frac{1}{3}

Decimal Notation

0.33333 \dots

Solution steps

x \to 1 lim (\frac{x + 1}{6 x ^{2} + 3 + 3 x})

Plug in the value

x = 1

= \frac{1 + 1}{6 \cdot 1 ^{2} + 3 + 3 \cdot 1}

Simplify

\frac{1 + 1}{6 \cdot 1 ^{2} + 3 + 3 \cdot 1} : \frac{1}{3}

= \frac{1}{3}

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

x \to - 2 lim (\frac{x}{x - 2})

x \to 5 lim (x + x^{2})

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

x \to \frac{π}{4} lim (\frac{tan ( x )}{x})

What is the limit as x approaches 1 of (x+1)/(sqrt(6x^2+3)+3x) ?
The limit as x approaches 1 of (x+1)/(sqrt(6x^2+3)+3x) is 1/3