Question

Determine the following limits
the limit as x approaches 9 of (9-x)/(3-sqrtx)

Answer 1

\[\large \lim_{x\rightarrow 9} \frac{9-x}{3-\sqrt{x}}\] Multiply the numerator and denominator by the conjugate.

Answer 2

So...\[\lim_{x\rightarrow 9} \left[\frac{9-x}{3-\sqrt{x}} \cdot \frac{3+\sqrt{x}}{3+\sqrt{x}}\right]\]

Answer 3

rewrite the numerator as the difference of 2 squares

\[\lim_{x \rightarrow 9} \frac{9 - (\sqrt{x})^2}{3 - \sqrt{x}}\]

factor the numerator... and things will become obvious...

Answer 4

Ahh...several methods of approach!