Question

lim x tends to 0
x÷sin5x​

Answer 1

Step-by-step explanation:

lim x tends to 0

x/sin5x

then first try to solve with directly

i.e

$lim \: x \: tends \: to \: 0 \: \frac{x}{ \sin(5x) } \\ = \frac{0}{ \sin(0) } = \frac{0}{0} \\ the \: value \: becomes \: \frac{0}{0} then \\ multipling \: \frac{x}{ \sin(5x) } \: by \: \sin(5x) \\ we \: get \\ lim \: x \: tends \: to \: 0 \: \frac{x}{ \sin(5x) } \times \sin(5x) \\ = \frac{x \times \sin(5x) }{ \sin(5x) } \\ = \frac{x}{ \sin } \times \frac{ \sin(5x) }{5x} \\ = \frac{x}{ \sin } \times 1$