Use l’Hospital’s rule, if applicable, to find the limit.

Find the equation of the tangent line at the given point on the curve.x2 + y2 + 2y = 0; (0, -2)

Find the indicated absolute extremum as well as all values of x where it occurs on the specified domain.f(x) = x3 – 3×2; [0, 4]Minimum

Assume x and y are functions of t. Evaluate dy/dt.xy + x = 12; dx/dt = -3, x = 2, y = 5

Solve the problem.Find two numbers x and y such that their sum is 420 and x2y is maximized.

Find the indicated absolute extremum as well as all values of x where it occurs on the specified domain.f(x) = x3 – 2×2 + 3x – 4; [-2, 5]Minimum

Solve the problem.A local office supply store has an annual demand for 40,000 cases of photocopier paper per year. It costs per year to store a case of photocopier paper, and it costs to place an order. Find the optimum number of cases of photocopier paper per order. Hint: Use formula from the critical point theorem.

Solve the problem.Find the elasticity of demand E for the demand function

What is the expected major product of the reaction shown?

Why does cyclohexanol have a pKa of 18 and phenol, despite its similarities in structure, have a pKa of 10?