Login / Register

List of top Mathematics Questions on Limit and Continuity

If \( z_r = \cos \frac{r\alpha}{n^2} + i \sin \frac{r\alpha}{n^2} \), where \( r = 1, 2, 3, ..., n \), then the value of \( \lim_{n \to \infty} z_1 z_2 z_3 ... z_n \) is:
Evaluate the limit: \[ L = \lim_{x \to 0} \frac{35^x - 7^x - 5^x + 1}{(e^x - e^{-x}) \ln(1 - 3x)} \]
If \( f(x) = \ln \left( \frac{x^2 + e}{x^2 + 1} \right) \), then the range of \( f(x) \) is: