Question

If lim(x→0)((cos4x + acos2x + b)/x4) is a finite quantity, find the value of a2 + b2 + 10.

Answer 1

We have

lim(x→0)((cos4x + acos2x + b)/x4)

Since it has a finite limit, so a + b + 1 = 0 ...(i)

Since, it has a finite limit,

so – 16 – 4a = 0

4a = – 16 ⇒ a = – 4

when a = – 4, b = 3

Hence, the value of a2 + b2 + 10

= 16 + 9 + 10

= 35.