1. The problem is to understand and practice limits involving indeterminate forms such as $\frac{0}{0}$ or $\frac{\infty}{\infty}$.\n\n2. Indeterminate forms occur when direct substitution in a limit leads to expressions like $0/0$, $\infty/\infty$, $0 \times \infty$, $\infty - \infty$, $0^0$, $1^\infty$, or $\infty^0$. These forms do not give enough information to determine the limit directly.\n\n3. One common method to resolve indeterminate forms is L'Hôpital's Rule, which states that if $\lim_{x \to a} f(x) = 0$ and $\lim_{x \to a} g(x) = 0$ or both approach $\pm \infty$, then $$\lim_{x \to a} \frac{f(x)}{g(x)} = \lim_{x \to a} \frac{f'(x)}{g'(x)}$$ provided the latter limit exists.\n\n4. Practice questions:\n\n(1) Evaluate $\lim_{x \to 0} \frac{\sin x}{x}$.\n\n(2) Evaluate $\lim_{x \to 0} \frac{1 - \cos x}{x^2}$.\n\n(3) Evaluate $\lim_{x \to \infty} \frac{e^x}{x^2}$.\n\n(4) Evaluate $\lim_{x \to 0} x \ln x$.\n\n(5) Evaluate $\lim_{x \to 1} \frac{x^x - 1}{x - 1}$.\n\n5. These problems involve indeterminate forms like $\frac{0}{0}$ or $0 \times (-\infty)$ and require algebraic manipulation, L'Hôpital's Rule, or rewriting expressions to find the limit.\n\n6. For example, in (1), direct substitution gives $\frac{0}{0}$, so we use the known limit or L'Hôpital's Rule to find the answer is 1.\n\n7. In (4), rewriting $x \ln x$ as $\frac{\ln x}{1/x}$ transforms the product into a quotient, allowing L'Hôpital's Rule to be applied.\n\nThese practice questions will help you recognize and solve limits involving indeterminate forms.