What is the limit as x approaches 3 of (sqrt(x^2+40)-7)/(x-3) ?

The limit as x approaches 3 of (sqrt(x^2+40)-7)/(x-3) is 3/7

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limit as x approaches 3 of (sqrt(x^2+40)-7)/(x-3)

x \to 3 lim (\frac{x ^{2} + 40 - 7}{x - 3})

\frac{3}{7}

Decimal Notation

0.42857 \dots

Solution steps

x \to 3 lim (\frac{x ^{2} + 40 - 7}{x - 3})

Rationalize numerator

\frac{x ^{2} + 40 - 7}{x - 3} : \frac{x + 3}{x ^{2} + 40 + 7}

= x \to 3 lim (\frac{x + 3}{x ^{2} + 40 + 7})

Plug in the value

x = 3

= \frac{3 + 3}{3 ^{2} + 40 + 7}

Simplify

\frac{3 + 3}{3 ^{2} + 40 + 7} : \frac{3}{7}

= \frac{3}{7}

x \to \frac{π}{2} lim (\frac{sin ( x )}{cos ( x )})

x \to π lim (\frac{sin ( x )}{2 + cos ( x )})

x \to - 1 lim (6 x^{3} - 7 x + 12)

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

x \to 0 + lim (3 (tan (x))^{x})

What is the limit as x approaches 3 of (sqrt(x^2+40)-7)/(x-3) ?
The limit as x approaches 3 of (sqrt(x^2+40)-7)/(x-3) is 3/7