Solve for: limit as x approaches 0 of (sin(x)+sin(5x))/(6x)

  1. Home
  2. Calculus
  3. Solve for: limit as x approaches 0 of (sin(x)+sin(5x))/(6x)

Expression: $\lim _{x\to 0}(\frac{\sin(x)+\sin(5x)}{6x})$

$\lim_{x\to{a}}[c\cdot{f(x)}]=c\cdot\lim_{x\to{a}}{f(x)}$

$=\frac{1}{6}\cdot \lim _{x\to 0}(\frac{\sin(x)+\sin(5x)}{x})$

Apply L'Hopital's Rule

$=\frac{1}{6}\cdot \lim _{x\to 0}(\frac{\cos(x)+\cos(5x)\cdot 5}{1})$

Plug in the value $ x=0$

$=\frac{1}{6}\cdot \frac{\cos(0)+\cos(5\cdot 0)\cdot 5}{1}$

Simplify $\frac{1}{6}\cdot \frac{\cos(0)+\cos(5\cdot 0)\cdot 5}{1}:{\quad}1$

$=1$

Random Posts
Random Articles