Math calculus 1

Question

If a

 and b

 are constants and

lim x→0 5a xcos(x)+btan(5x)

tan(5x)+2sin(10x) =  6,

then a+b=

Answer 1

Plug in 0. You get 0/0 which means you have to use l'hopital's rule.

Take the derivative of the top and bottom

lim x→0 [-5axsin(x) + 5acos(x) + 5bsec²(5x) ] / [ 5sec²(5x) + 20cos(10x) ] = 6

Plug in 0

(5a + 5b) / 25 = 6

(a + b) / 5 = 6