In the realm of calculus, L'Hospital's Rule plays a crucial role in evaluating limits that manifest in indeterminate forms such as 0/0 or ∞/∞. This rule asserts that the limit of the ratio of two functions, as x closes in on a specific value, is equivalent to the limit of the ratios of their respective derivatives, given that specific criteria are satisfied.
| Topic | Problem | Solution |
|---|---|---|
| None | Evaluate the limit \(\lim_{{x \to 0}} \frac{{e^x … | Step 1: Notice that the limit is in the indeterminate form \(\frac{0}{0}\) as \(x\) approaches \(0\… |
| None | 3. For what values of $a$ and $b$ is the function… | The function is continuous if the limit from the left and right at the points of discontinuity are … |
| None | Determine whether the following function is conti… | To determine whether the function is continuous at a given point, we need to check three conditions… |