Exams › JEE Main › Maths

If the function f defined as f(x) = 1/x − (k − 1)/(e^(2x) − 1), x ≠ 0, is continuous at x = 0, then the ordered pair (k, f(0)) is equal to ?

1. (3, 1)
2. (3, 2)
3. (1/3, 2)
4. (2, 1)

Correct answer: (3, 1)

Solution

The function is continuous at x = 0 if the limit as x approaches 0 equals the function value at that point. By evaluating the limit of f(x) as x approaches 0, we find that it converges to 1 when k is set to 3, thus making the ordered pair (3, 1) the correct choice.

Related JEE Main Maths questions

• Suppose f(x)=α(x)β(x)γ(x) for every real x, where α(x), β(x), and γ(x) are differentiable. If f'(2)=18f(2), α'(2)=3α(2), β'(2)=-4β(2), and γ'(2)=kγ(2), then what is the value of k?
• For the piecewise-defined function f(x) = { [sin((a+1)x) + sin x]/x, x < 0; c, x = 0; [√(x + bx²) - √x]/(b x^(3/2)), x > 0 } to be continuous at x = 0, which values of a, b, and c are required?
• Let f(x) and g(x) be continuously differentiable functions such that f'(x) = g(x) and f''(x) = -f(x). Define h(x) = [f(x)]² + [g(x)]². If h(0) = 5, what is the value of h(10)?
• For what value of p can the function f(x) = { ((4^x - 1)³)/(sin x · [log|1 + x²/3|]^p), x ≠ 0; 12(log 4)³, x = 0 } be made continuous at x = 0?
• Consider the function f: R -> R given by f(x) = max{x, x³}. At which points is f(x) not differentiable?
• Consider the function f(x)=[(1-sin³ x)/(3cos² x),, x<(π)/(2),; [4pt] p,, x=(π)/(2),; [4pt] q(1-sin x),, x>(π)/(2).] If f is continuous at x=(π)/(2), then the pair (p,q) is

⚔️ Practice JEE Main Maths free + battle 1v1 →