Question

lim as x - -> 0 (1-cos5xcos7x)/((sin11x)^@)

Answer 1

answer is 0

Answer 2

let me check it once more

Answer 3

i want to know how did u find out the answer???please!

Answer 4

what is "^@"

Answer 5

I am sorry, the answer is 37 / 121, but the algebra is tiresome

Answer 6

give me some time to post the full solution.

Answer 7

Since, Cos C + Cos D = 2.cos ((C + D) / 2)cos ((C -D) / 2)

\[1 - \cos5x.\cos7x = 1 - (1/2) (\cos12x + \cos 2x)\]
= 1/2(1 - COS12X) + 1/2 (1 - COS2X) = (1/2).2(SIN6X)^2 + (1/2).2(SINX)^2 = (SIN6X) ^ 2 + (SINX)^2

Hence the equation becomes -\[\sin ^{2}6x / \sin ^{2}11x + \sin ^{2}x/\sin ^{2}11x\]
The first part \[= [(\sin ^{2}6x / (6x)^{2}) / (\sin ^{2}11x / (11x) ^{2})] (36 /121)\]

Did you understand this part? (36 / 121 is introduced to nullify (6x)^2 and (11x)^2)

Hence the first part becomes 36 / 121

Similarly the second part becomes 1 / 121

Hence it becomes in total = 37 / 121

Answer 8

yep, L'Hopitals Rule twice ---> limit = 37/121

Answer 9

yeah, that is much easier :)

Answer 10

nice solution

Answer 11

I will not forget L'Hospital anymore

Answer 12

understood all part you had written. thank you very much for your help.

Answer 13

do u have anything solution?

Answer 14

I am sorry, but could not understand your question :), seemingly I dont have solution to this question

Answer 15

((sin11x)^2)