Question

any body help me how to solve lim x->0 (sin4x)/x

Answer 1

follow your last post.

Answer 2

i cant understand how>?

Answer 3

do u know this standard limit :
\(\lim \limits_{x \rightarrow0}\frac{\sin x}{x}=1\)

Answer 4

yes i konw that

Answer 5

i cant use l hospital rules

Answer 6

in my book answer is 4
i dont know how??

Answer 7

so, do this , multiply the numerator and denominator by 4
\(\huge 4\lim \limits_{x \rightarrow0}\frac{\sin 4x}{4x}=...?\)

Answer 8

\(\huge 4\lim \limits_{4x \rightarrow0}\frac{\sin 4x}{4x}=...?\)
now put 4x = y
and you get a standard limit whose value is 1 (with 4)

Answer 9

if i multiply that what did i got?

Answer 10

\[\lim_{x \rightarrow 0} \sin\] i got

Answer 11

what! ? how ??

Answer 12

can you give me full steps:

Answer 13

let y=4x
\(\large 4\lim \limits_{4x \rightarrow0}\frac{\sin 4x}{4x}=4[\lim \limits_{y \rightarrow0}\frac{\sin y}{y}]= 4(..?..)\)

Answer 14

1you mean?

Answer 15

yes, ?=1
so, 4*1=4

Answer 16

\[4\lim4x→0\sin4x4x=4[limy→0sinyy]=4(1)= than is equal \to 4\]

Answer 17

thank you soo much

Answer 18

hmm...welcome ^_^