Question

I need help on 3,4,5,6,7,8 if you can show me the steps

Answer 1

The easiest way to find such limits, where there is a numerator and a denominator is to apply Hospital's Rule.
1st find the derivative of the numerator and the derivative of the denominator, if it still gives an indeterminate value, find the second derivative of N and D

3) lim sin(2x)/x when x →0
 Derivative sin2x → 2cos2x
 Derivative x→ 1
 2cos2x/1 when x→0 , 2cos2x → 2
 and lim sin(2x)/x when x →0 is 2

4) lim(sinx)/(2x²-x)

→cosx/(2x-1) when x →0 cosx/(2x-1) = -1
and lim(sinx)/(2x²-x) when x →0 is -1

and so on and so forth. Try to continue following the same principle