Functions: Equation of Tangent Line

Find the equation of the line tangent to the graph of f(x)=x^3+x at the point (-1,-2).

word problem derivatives

A ball is dropped from the top of a building which is 1000 feet tall. GIVEN (s(t)=-16t^2+v(initial)t+s(initial)) A. Write the position and velocity functions for the ball. B. Find the instantaneous velocity went t = 2 seconds. C. How long does it take the ball to reach the ground. Please solve using calculus (derivativ ...continues

Implicit Differentiation

Find dy/dx implicitly: x^2+6xy-5y+y^3=12

Proof that the derivative of the inverse cosine of x = -1/ sqrt(1-x^2)

The inverse cosine function has domain [-1,1] and range [0, pi]. Prove that (cos^-1)'(x) = -1 / sqrt(1-x^2)

Critical points of a polynomial of degree 3.

Give examples of polynomials of degree 3 that have no critical point, only one critical point, and two critical points.

Double Integral : Integrating with respect to two variables.

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Mass and centroid of a Plane Lamina

Please see the attached file for the fully formatted problem. Find the mass and centroid of a plane lamina with the given shape and density delta, the region bounded by y = x2 and x = y2 delta(x,y) = x2 + y2.

Volume and Centroid of an Ice Cream Cone (Sphere on top of Cone).

Please see the attached file for the fully formatted problems. Find the volume and centroid of the ice cream cone.

Average distance from a point on a disk.

Please see the attached file for the fully formatted problem. Show that the average distance of a point of a disk with radius a is...

Surface area of the part of a sphere that is inside a Cylinder

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