Question

If f(x) = sin(x)cos(x) and g(x) = x^2 than find value of limx → 0⁡ ^f(x)⁄g(x)

(a) 2

(b) 0

(c) -1

(d) Cannot be found

I have been asked this question by my college director while I was bunking the class.

The origin of the question is Indeterminate Forms in chapter Differential Calculus of Engineering Mathematics

Answer 1

The correct answer is (b) 0

To explain I would say: \(\lim_{x\rightarrow 0}\frac{f(x)}{g(x)}=\lim_{x\rightarrow 0}\frac{sin(x)cos(x)}{x^2}\) = 0/0

Henece, by L’Hospital rule

\(\lim_{x\rightarrow 0}\frac{f(x)}{g(x)}=\lim_{x\rightarrow 0}\frac{cos(2x)}{2x}=\frac{1}{0}\)

Again by L’Hospital rule

\(\lim_{x\rightarrow 0}\frac{f(x)}{g(x)}=\lim_{x\rightarrow 0}\frac{sin(2x)}{1}=0\)