Consider the following trajectory of a moving object.
r (t) = eᵗ sin (t), eᵗ cos (t), 5eᵗ
Find the tangential and normal components of the acceleration.

Write the expression 7x^3-28xy^2 as the product of 3 factors

Does the function satisfy the hypotheses of the mean value theorem on the given interval? f(x) = 4x^2 + 3x + 4, [−1, 1] no, f is continuous on [−1, 1] but not differentiable on (−1, 1). no, f is not continuous on [−1, 1]. yes, f is continuous on [−1, 1] and differentiable on (−1, 1) since polynomials are continuous and differentiable on . there is not enough information to verify if this function satisfies the mean value theorem. yes, it does not matter if f is continuous or differentiable; every function satisfies the mean value theorem.

Find the area of the triangle formed by the origin and the points of intersection of parabolas y=−3x^2+20 and y=x^2−16.