Calculus: Derivatives & Integrals

What is the limit of $\frac{\sin x}{x}$ as $x$ approaches $0$?

Which rule is applied to find the derivative of a composite function $f(g(x))$?

Which integration technique is most appropriate for evaluating $\int x e^{x^2} dx$?

The derivative of a constant function is zero.

The definite integral of a function between two points represents the area under the curve between those points.

Optimization problems in calculus often involve finding critical points where the derivative equals zero or does not exist.