List of top Mathematics Questions on Limits asked in KEAM

$\lim_{x \to 0} \frac{\log(1 + 3x^2)}{x(e^{5x} - 1)} =$

If $f(x) = \frac{x+2}{3x-1}$, then $f(f(x))$ is:

Let \( f(x) = (x^5 - 1)(x^3 + 1) \), \( g(x) = (x^2 - 1)(x^2 - x + 1) \) and let \( h(x) \) be such that \( f(x) = g(x)h(x) \). Then \( \lim_{x \to 1} h(x) \) is:

Let \( f(x) = (x^5 - 1)(x^3 + 1) \), \( g(x) = (x^2 - 1)(x^2 - x + 1) \) and let \( h(x) \) be such that \( f(x) = g(x)h(x) \). Then \( \lim_{x \to 1} h(x) \) is:

\( \lim_{x \to 0} \frac{\log(1 + 3x^2){x(e^{5x} - 1)} = \)}

If \( f(x) = \frac{x+2{3x-1} \), then \( f(f(x)) \) is:}

Let \( f(x) = (x^5 - 1)(x^3 + 1) \), \( g(x) = (x^2 - 1)(x^2 - x + 1) \) and let \( h(x) \) be such that \( f(x) = g(x)h(x) \). Then \( \lim_{x \to 1} h(x) \) is:

\( \lim_{x \to 0} \frac{\log(1 + 3x^2){x(e^{5x} - 1)} = \)}

If \( f(x) = \frac{x+2{3x-1} \), then \( f(f(x)) \) is:}