If lim x$\to$0$cos(2x)+a$$cos(4x)-b$is finite, then$(a + b)$is equal to : 4 x
Step-by-Step Solution
Key Concept: Expand the expression near the limiting point using the appropriate standard trigonometric, logarithmic, or exponential approximation.
lim x$\to$0 cos$2x+a$cos$4x-b$$4 = finite$x (1) { ⎪ 2 4 (2x) (2x) 1 - + 2 2 (4x)4 (4x) ⎪ – 4⋯$}}+a{1$- +$\ldots$$\cdot$}-b – 2 ⌊4 –$L = 4$x 2 4 2 32 6$(1 + a - b) - x$$(2 + 8a) + x$$( + a) + x$()$\ldots$3 3$L = 4$x 1 ∴$1 + a - b = 0$and$2 + 8a = 0$$\Rightarrow$ a = - 4$b = a + 1$1 3 = - +$1 = 4$4 1 3 1 ∴$a + b$= - + = 4 4 2
Correct Answer: 1