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

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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})

1

Solution steps

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

Rationalize denominator

\frac{x + 1}{6 x ^{2} + 3 + 3 x} : - \frac{- 3 x + 6 x ^{2} + 3}{3 ( x - 1 )}

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

Plug in the value

x = - 1

= - \frac{- 3 ( - 1 ) + 6 ( - 1 ) ^{2} + 3}{3 ( - 1 - 1 )}

Simplify

- \frac{- 3 ( - 1 ) + 6 ( - 1 ) ^{2} + 3}{3 ( - 1 - 1 )} : 1

= 1

\int 2 x sec^{2} (3 x) d x

\int_{0}^{2} \frac{x}{1 + x ^{2}} d x

\frac{d}{d x} f (x) = 3 x^{2} - 5 x + 2

\frac{d y}{d x}, x^{5} y + 5 x y^{5} = x + y

x \to 2 + lim (cos (x - 2))

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