Limits and Derivatives · Question 17

If x 0 (2x) + a (4x) - bx4 is finite, then (a + b) is equal to:

1. 0
2. 34
3. -1
4. 12

Answer

(4) 12

Solution

= 1 - 22 + 424 -

2x = 1 - 2x2 + 23x4 -

4x = 1 - 8x2 + 323x4 -

Numerator = (1 + a - b) - (2 + 8a)x2 + ( 23 + 32a3 )x4 -

For the limit to be finite, the coefficients of x0 and x2 must vanish:

2 + 8a = 0 a = - 14

1 + a - b = 0 b = 34

a + b = - 14 + 34 = 12

Answer: (4)