Question

lf $\underset{x\to 0}{lim}\left(\frac{\cos 4x+a\cos 2x+b}{x^4}\right)$ is finite then the value of $a,b$ respectively are

• A. $5-4$
• B. $-5,-4$
• C. $-4,3$
• D. $4,5$

Answer 1

The correct option is C $-4,3$

${lim}_{x\to 0}\left(\frac{\cos 4x+a\cos 2x+b}{x^4}\right)$

As $x\to 0$, denominator tends to 0, so the numerator also tends to 0.

$\Rightarrow {lim}_{x\to 0}\cos 4x+a\cos 2x+b=0$

at $x=0\Rightarrow \cos 4x=1,\cos 2x=1$

$\Rightarrow 1+a+b=0$

$\Rightarrow a+b=-1$

Now, put $a=-4$

$\Rightarrow b=3$

Option C satisfies above equation.