Question

lim x tends to 0 √1+2x-√1-2x/sinx

Answer 1

• The given question is lim x tends to 0 √1+2x-√1-2x/sinx

• If we substitute the value of x=0 in numerator and denominator, we get the indeterminate form 0/0 .
• We should use L'hopital's rule.
• By differentiating both the numerator and denominator, and replacing the value of x=0, we get the answer as 4 .

• $\lim_{x \to 0} \frac{\sqrt{1+2x}-\sqrt{1-2x} }{sin x}$

• = $\lim_{x \to 0} \frac{\frac{2}{ \sqrt{1+2x}}+\frac{2}{\sqrt{1-2x}} }{cos x}$

• = 4 .