Calculus Examples

$lim_{x \to 0} (3 x) \sin (\frac{1}{x})$

Step 1

Move the term $3$ outside of the limit because it is constant with respect to $x$ .

$3 lim_{x \to 0} x \sin (\frac{1}{x})$

Step 2

Since $x \cdot - 1 \leq x \sin (\frac{1}{x}) \leq x \cdot 1$ and $lim_{x \to 0} x \cdot - 1 = lim_{x \to 0} x \cdot 1 = 0$ , apply the squeeze theorem.

$3 \cdot 0$

Step 3

Multiply $3$ by $0$ .

$0$