Question

lim x->0 sin4x/x , can somone help me solve this step by step ?? thanks

Answer 1

sorry i mean sin4x/7x

Answer 2

\[\lim_{x\to 0}\frac{\sin(4x)}{7x}=\lim_{x\to 0}\frac{4}{7}\frac{\sin(4x)}{4x}\]

Answer 3

ok then ??

Answer 4

do you know this limit

\[\lim_{x\to 0}\frac{\sin(x)}{x}\]

Answer 5

yes that equals to 1 , so i am assuming the answer is 4/7?

Answer 6

yes

Answer 7

how should i write it ?

Answer 8

could u contunie the steps , becuz my teacher is a hard marker

Answer 9

\[\lim_{x\to 0}\frac{4}{7}\frac{\sin(4x)}{4x}\]

let \(t=4x\)

then as \(x\to 0\) we have \(t\to 0\)

and thus

\[\lim_{x\to 0}\frac{4}{7}\frac{\sin(4x)}{4x}=\lim_{t\to 0}\frac{4}{7}\frac{\sin(t)}{t}=\frac{4}{7}\times 1\]
\[=\frac{4}{7}\]

Answer 10

could u help me solve one more??

Answer 11

tanx/3x

Answer 12

same idea

\[\frac{\tan(x)}{3x}=\frac{\sin(x)/\cos(x)}{3x}=\frac{\sin(x)}{3x}\frac{1}{\cos(x)}\]

now do what I did above

Answer 13

\[=\frac{1}{3}\frac{\sin(x)}{x}\frac{1}{\cos(x)}\]

Answer 14

i know the fist funstion equals 1 what about 1/cosx?

Answer 15

@Zarkon

Answer 16

is \(x\to 0\)?

Answer 17

yes

Answer 18

what is \(\cos(0)\)?

Answer 19

1?

Answer 20

yes

Answer 21

so their both equal to 1 ?? and so the answer is 1/3??

Answer 22

yes