Exams › JEE Main › Maths

lim x→0 (sin²x)/(√2 − √(1 + cos x)) equals -

1. 4
2. 2√2
3. 4√2
4. √2

Correct answer: 4√2

Solution

To evaluate the limit, we can use L'Hôpital's rule since both the numerator and denominator approach 0 as x approaches 0. After applying the rule and simplifying, we find that the limit equals 4√2.

Related JEE Main Maths questions

• Evaluate the limit as x approaches 0: ((1+tan x)/(1+sin x))^(csc x).
• Evaluate the limit as x approaches 0 of sin([x−3]) divided by [x−3], where [.] denotes the greatest integer function.
• Evaluate the limit as x approaches 0: (sin(x⁴) − x⁴ cos(x⁴) + x²⁰) / (x⁴(e^(2x⁴) − 1 − 2x⁴)).
• Evaluate the limit lim_(n→∞)(n³-8)/(n³+8). What is its value?
• If lim_(x→∞) (1+(λ)/(x)+(μ)/(x²))^(2x)=e², which of the following values of λ and μ is correct?
• Consider the following statements: Statement 1: If lim_(x→α)(sin(f(x)))/(x-α), where f(x)=ax²+bx+c, exists as a finite nonzero number, then lim_(x→α)(1/f(x)-1)/(1/f(x)+1) does not exist. Statement 2: The limit lim_(x→α)(sin(f(x)))/(x-α) can be finite only in the indeterminate form 0/0.

⚔️ Practice JEE Main Maths free + battle 1v1 →