Blog

Given (10 pts) Show your work in the upload submission.  Input the final answer in the given space below.  (1 pt) Find the derivative of the function using the definition of derivative. (1 pt) Find an equation of the tangent line (in slope-intercept form) to the graph of at x=-1. (1 pt) Find the point(s), as an ordered pair, on the graph of at which the tangent line is horizontal, if any.

Use the linear approximation or differentials, whichever you prefer, to approximate the number  . Round to 4 decimal places. (4 pts) Show your work in the upload submission. (1 pt) Input the final answer in the given space below. 

Use the linear approximation or differentials, whichever you prefer, to approximate the number  . Round to 4 decimal places. (4 pts) Show your work in the upload submission. (1 pt) Input the final answer in the given space below. 

A boat travels north from a dock at 12 mph. Three hours later, a second boat leaves the same dock, sailing west at 16 mph. How fast are the boats moving apart when the second boat has been sailing for 2 hours? Round the answer to the nearest hundredth. Clearly show your work in the upload submission: (2 pts) Draw a diagram and label all the known values and unknown values (e.g., x, y, z, etc) (4 pts) Show your calculations in the upload submission. Make sure to clearly show how you form the function that you use to obtain your answer. (2 pts) Enter your answers in the space below, using the correct units when necessary. Use ^ to denote exponents, for example, type x^3 for x³. Round your answer to two decimal places. The function you use to find the rate [a] The rate at which the boats are moving apart is [b] when the second boat has been sailing for 2 hours.

For the following function (7 pts) Show your work in the upload submission. Input the final answer in the given space below. (1 pt) Find the derivative. Show the use of chain rule clearly and simplify your answer.

The height (in meters) of a projectile shot vertically upward from a point 3 m above ground level with an initial velocity of 23.5 m/s is after t seconds. (11 pts) Show your work in the upload submission. Input the final answer in the given space below. (Round your answer to two decimal places) (1 pt) The velocity after 4 seconds is [a]. (1 pt) The time the projectile reaches its maximum height is [b]. (1 pt) The maximum height is [c]. (1 pt) The time it hits the ground is [d]. (1 pt) The velocity when it hits the ground is [e].

Given  (6 pts) Use the limit definition of a derivative at a point to show that f is not differentiable at a=-3 (in upload submission only). (4 pts) Sketch the graph of f and f ‘ (in upload submission only). Input the final answer in the given space below.  (2 pts) The interval(s) on which f is continuous is [a]. (2 pts) The interval(s) on which f is differentiable is [b]. (2 pts) True/False? [c]. If a function is continuous on an interval (a,b), then it is differentiable on (a,b). If the statement is false, provide a specific counterexample. [d]

Use the two special trigonometric limits in Chapter 2 and other limit laws to find the limit below (4 pts) Show your work in the upload submission. (1 pt) Input the final answer in the given space below.

A rock is thrown upward from the surface of Mars with velocity of 20 m/s, its height (in meters) after t seconds is   (11 pts) Show your work in the upload submission. Input the final answer in the given space below. (Round your answer to two decimal places) (1 pt) The velocity of the rock after 6 seconds is [a]. (1 pt) The time the rock reaches its maximum height is [b]. (1 pt) The maximum height is [c]. (1 pt) The time it hits the ground is [d]. (1 pt) The velocity when it hits the ground is [e].     

Which of the following correctly describe characteristics of reinforcement learning that distinguish it from supervised learning? Select all that apply.