Question

Find \(lt_{x\rightarrow 0}\frac{2cos(2x)+3cos(5x)-5cos(19x)}{cos(4x)-cos(3x)}\)

(a) -76

(b) -6

(c) -7

(d) 0

I had been asked this question in semester exam.

My question is based upon Indeterminate Forms topic in division Differential Calculus of Engineering Mathematics

Answer 1

Correct choice is (a) -76

For explanation: Form here ^0⁄0

Applying L hospitals rule we have

\(=lt_{x\rightarrow 0}\frac{4cos(2x)+15cos(5x)-95cos(19x)}{4cos(4x)-3cos(3x)}\)

\(\frac{4+15-95}{4-3}\) = -76.