Word Problem : Intermediate Value Theorem

At 8am on Saturday, a man begins running up the side of a mountain to his weekend campsite. On Sunday at 8am, he runs back down the mountain. It takes him 20 minutes to run up, but only 10 minutes to run down. At some point on his way down, he realizes that he passed the same exact place at exactly the same time on Saturday. ...continues

Sets : Intermediate Value Theorem

Prove that the interval (0,2)~R. Use the Intermediate Value Theorem.

Proportionality and Rate of Change Word Problem

A container has the shape of an open right circular cone. The height of the container is 10cm and the diameter of the opening is 10cm. Water in the container is evaporating so that its depth h is changing at the constant rate of -3/10 cm/hr. Show that the rate of change of the volume of water in the container due to evaporati ...continues

Evaluating Functions using Derivatives

Let f be a function that is differentiable for all real numbers. The table gives the values of f and its derivative f' for selected points x in the closed interval -1.50 for -1.5 ...continues

Graph : Convert to Rectangular Form

Let x=cosTheta and y=3sinTheta for0<=Theta<=Pi a.Sketch the graph b.Convert to rectangular form

Graphs : Rectangular and Parametric Forms

Graph x=(t^2+2t+1)^(1/2) y=(t^3+2t^4)/t^2 a. Graph on the interval [0,3] b. Convert to rectangular form. c. Adjust the domain of the rectangular form to agree the parametric form.

Comparing Graphs : First and Second Derivatives

x -1.5 -1.0 -0.5 0 0.5 1.0 1.5 f(x) -1 -4 -6 -7 -6 1.0 -7 f'(x) -7 -5 -3 0 3 5 7 Let f be a function that is differentiable for all real numbers. The table above gives the values of f and its derivative f' for selected points x in the closed interv ...continues

Geometric series?

Determine if the following series converges and if possible give its sum 2/3 + 2/9 + 2/27 + 2/81 + ...

Seven Calculus Problems

Please see the attached file for the fully formatted problems. 1. Use an iterated integral to find the area of a region... 2. Evaluate the double integral... 3. Use double integral to find the volume of a solid... 4. Verify moments of inertia... 5. Limit of double integral... 6. Surface area... 7. Triple integral...

Double Integrals

Please see the attached file for the fully formatted problem. Use the indicated change of variables to evaluate the double integral: SR S 60xy dA x = 1/2(u + v) y = -1/2(u - v)