What is the limit as x approaches sqrt(2) of (x^2-2}{\frac{5x)/7-(5sqrt(2))/7} ?

The limit as x approaches sqrt(2) of (x^2-2}{\frac{5x)/7-(5sqrt(2))/7} is (14sqrt(2))/5

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limit as x approaches sqrt(2) of (x^2-2}{\frac{5x)/7-(5sqrt(2))/7}

x \to 2 lim (\frac{x ^{2} - 2}{\frac{5 x}{7} - \frac{5 2}{7}})

\frac{14 2}{5}

Decimal Notation

3.95979 \dots

Solution steps

x \to 2 lim (\frac{x ^{2} - 2}{\frac{5 x}{7} - \frac{5 2}{7}})

Simplify

\frac{x ^{2} - 2}{\frac{5 x}{7} - \frac{5 2}{7}} : \frac{7}{5} (x + 2)

= x \to 2 lim (\frac{7}{5} (x + 2))

Plug in the value

x = 2

= \frac{7}{5} (2 + 2)

Simplify

\frac{7}{5} (2 + 2) : \frac{14 2}{5}

= \frac{14 2}{5}

\frac{d ^{2}}{d x ^{2}} ((x^{2} + 5)^{5})

\frac{d}{d x} (\frac{x - 5}{x ^{2}})

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

2 y

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

What is the limit as x approaches sqrt(2) of (x^2-2}{\frac{5x)/7-(5sqrt(2))/7} ?
The limit as x approaches sqrt(2) of (x^2-2}{\frac{5x)/7-(5sqrt(2))/7} is (14sqrt(2))/5