Direct substitution into a limit gives $\frac{0}{0}$. What does this tell you?

The form is indeterminate; rewrite the function

Which technique best fits $\lim_{x \to 0} \frac{\sqrt{x + 9} - 3}{x}$?

Multiply by the conjugate $\sqrt{x+9} + 3$

The limit is infinite (does not exist as a finite value)

$\sqrt{x^2} = |x|$, which equals $-x$ as $x \to -\infty$

The exam awards the algebraic method and justification, not only the final value

13questions. Pick an answer and you'll see why right away.

What should always be your first step when evaluating a limit?
Direct substitution into a limit gives $\frac{0}{0}$ . What does this tell you?
Evaluate $\lim_{x \to 5} \frac{x^2 - 25}{x - 5}$ .
Which technique best fits $\lim_{x \to 0} \frac{\sqrt{x + 9} - 3}{x}$ ?
What is $\lim_{x \to 0} \frac{\sin x}{x}$ (with $x$ in radians)?
Evaluate $\lim_{x \to 0} \frac{\sin 5x}{x}$ .
Substitution into $\lim_{x \to 3} \frac{x + 1}{x - 3}$ gives $\frac{4}{0}$ . What is the correct conclusion?
For $\lim_{x \to 2^+} \frac{1}{x - 2}$ , what is the sign of the result?
Evaluate $\lim_{x \to \infty} \frac{4x^2 + 1}{2x^2 - x}$ .
What is $\lim_{x \to \infty} \frac{3x + 2}{x^2 + 1}$ ?
When evaluating $\lim_{x \to -\infty} \frac{x}{\sqrt{x^2 + 1}}$ , what key fact about $\sqrt{x^2}$ must you use?
Evaluate $\lim_{x \to 2} \frac{\frac{1}{x} - \frac{1}{2}}{x - 2}$ .
On the no-calculator section, why can a correct numerical answer with no shown work lose points?