Question

limit-->0
sin(x^2)/3x^2

Answer 1

Separate the limit into the top and bottom, meaning focus on one part then the other.

Answer 2

Notice the bottom portion, 3x^2, will go to 0. This can be determined by a direction substitution to get 3(0)^2 = 0

Answer 3

The top, sin(x^2), can be determined the same way. Using direction subtitution, sin(0^2) = sin(0) = 0. thus, the limit converges to 0

Answer 4

substitution*
Notice, I broke it up into 2 parts. If you wish, you can directly substitute zero. Usually, that should be your go-to-solution. However, you have to learn to recognize when a direct substitution will work, and where it will not work.

Answer 5

I hope this helps!