1. ## limit problem

lim as x->0 of f(x) where f(x)= (1 /x^2)sin(x/2)

i plugged in numbers close to zero and discovered the limit to be 0.5 but how do i solve this algebraically.

2. Hello,
Originally Posted by myoplex11
lim as x->0 of f(x) where f(x)= (1 /x^2)sin(x/2)

i plugged in numbers close to zero and discovered the limit to be 0.5 but how do i solve this algebraically.
If it is indeed (1/x²)sin(x/2), then the limit is not 0.5, it's infinite >.>

If it is (1/x)sin(x/2), substitute t=x/2 (---> x=2t) and you'll find a limit you know.

If it is (1/x²)sin(x²/2), substitute t=x²/2.

3. Originally Posted by Moo
Hello,

If it is indeed (1/x²)sin(x/2), then the limit is not 0.5, it's infinite >.>

If it is (1/x)sin(x/2), substitute t=x/2 (---> x=2t) and you'll find a limit you know.

If it is (1/x²)sin(x²/2), substitute t=x²/2.
actually, in the first case, the limit doesn't exist. the one-sided limits are not equal