math calculus 1

Question

lim 5axcos(x)+btan(5x)÷tan(5x)+2sin(10x)=6 , when x goes to 0

what is a+b?

Answer 1

This is a 0/0 limit case, so we can use L'Hopital's rule.

Taking the derivative of the numerator and denominator:

lim (-5axsin(x) + 5acos(x) + 5bsec²(5x))/(5sec²(5x)+ 20cos(10x)) = 6

x→0

Taking the limit:

(0 +5a+5b)/(5+20) = 6

(5a+5b)/25 = 6

5a+5b = 150

a+b = 30