$\displaystyle\lim_{x\to0} \frac{\sin^{2}x}{\sqrt{2} - \sqrt{1+\cos x}} $ equals :
- $2 \sqrt{2}$
- $4 \sqrt{2}$
- $ \sqrt{2}$
- 4
The Correct Option is B
Solution and Explanation
$ = \frac{\left(1\right)^{2} .\left(2\sqrt{2}\right)}{\frac{1}{2}} = 4\sqrt{2}$
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Concepts Used:
Limits And Derivatives
Mathematically, a limit is explained as a value that a function approaches as the input, and it produces some value. Limits are essential in calculus and mathematical analysis and are used to define derivatives, integrals, and continuity.
Limits Formula:
Derivatives of a Function:
A derivative is referred to the instantaneous rate of change of a quantity with response to the other. It helps to look into the moment-by-moment nature of an amount. The derivative of a function is shown in the below-given formula.
Properties of Derivatives:
Read More: Limits and Derivatives