Working out limits: laws, 0 over 0 and sine
Work out limits of sums and products from graphs, open up the 0 over 0 form by factorising and cancelling, and meet the sine limit.
- France: grade 12
- Iran: grade 11
- Afghanistan: grade 12
- Syria: grade 11
- Palestine: grade 11
- Russia: grade 10
Guide
The limit of a sum, difference or product of two functions is the sum, difference or product of their limits: lim(f·g) = limf·limg. So read each function's limit separately.
If putting the number in gives 00, you do not have an answer yet. Factorise the top and the bottom, cancel the common factor that is zero, and put the number in again.
For small angles, sin x is almost x. That is why lim(x→0)sin x ÷ x = 1 and, for any number k, lim(x→0)sin kx ÷ x = k.