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

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

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limit as x approaches-3 of sqrt(x^2+x)-x

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

6 + 3

Decimal

5.44948 \dots

Solution steps

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

Plug in the value

x = - 3

= (- 3)^{2} - 3 - (- 3)

Simplify

(- 3)^{2} - 3 - (- 3) : 6 + 3

= 6 + 3

\int_{0}^{1} \frac{x}{x ^{3} + 1} d x

\frac{d}{d x} (\frac{x - 6}{x ^{2} - 2 x + 12})

x \to 0 lim (- 2 sin (x))

t an g e n t y = 3 x^{3} - 2 x, (1, 1)

x \to 0 lim (ln (- x))

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