Using 4 equal-width intervals, show that the trapezoidal rule is the average of the upper and lower sum estimates for the integral from 4 to 0 of x squared dx. (10 points)

Identify the graph of y = ln x + 1.

Prove the converse of the pythagorean theorem using similar triangles. the converse of the pythagorean theorem states that when the sum of the squares of the lengths of the legs of the triangle equals the squares length of the hypotenuse, the triangle is a right triangle. be sure to create and name the appropriate geometric figures.

Rewrite the polynomial -9x5 + 36x4 + 189x3 in factored form.