Calculus Practice

Evaluate: lim(x→2) (x² − 4) / (x − 2)

Evaluate using L'Hôpital\'s Rule: lim(x→0) (sin(3x)) / (5x)

Find dy/dx using the chain rule: y = (2x + 1)⁵

Find dy/dx implicitly: x² + y² = 25

A ladder 10 ft long leans against a wall. The bottom slides away at 1 ft/s. How fast is the top sliding down when the bottom is 6 ft from the wall?

Find the local minimum of f(x) = x³ − 3x + 2.

On what interval is f(x) = x³ − 6x² + 9x + 1 concave up?

Evaluate: ∫ 2x·cos(x²) dx

By the Fundamental Theorem of Calculus, evaluate: ∫₁³ (x² + 1) dx

Find the area between y = x and y = x² from x = 0 to x = 2.