Thread: limits help please!!!

i don't know how to prove the following limits

limit of ( 1 - cos x) / x^2 when x is +infinity

limit of (tan4x) / 6 when x is 0

limit of (sin x^2) / x

in the first equation i got to the point of multiplying by the reciprocal but i don't know what to do next

in the second equation i converted tan to sin/cos but i dont know where to go from there

Originally Posted by ubhutto

i don't know how to prove the following limits

limit of ( 1 - cos x) / x^2 when x is +infinity

limit of (tan4x) / 6 when x is 0

limit of (sin x^2) / x

in the first equation i got to the point of multiplying by the reciprocal but i don't know what to do next

in the second equation i converted tan to sin/cos but i dont know where to go from there

In the first, is bounded between 0 and 2, and the denominator goes to , which makes the fraction go to 0.

For the second, surely you can just substitute in x = 0.

For the third, what is the value of x going to?

it is going to 0

Well multiply top and bottom by x to give



Can you go from there?

i dont understand what to do with the sinx^2 / x^2 , how do i simplify it, if you can help me with that part ill be able to do the rest of the problems i have

Originally Posted by ubhutto

i dont understand what to do with the sinx^2 / x^2 , how do i simplify it, if you can help me with that part ill be able to do the rest of the problems i have

You should know that . Here your just happens to be .