Find the indicated derivative using differentiation rules (not limit definitions). Simplify when possible. (4 pts) Show your work in the upload submission.  (1 pt) Input the final answer in the given space below. 

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.

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]

Find the indicated derivative using differentiation rules (not limit definitions). Simplify when possible. (6 pts) Show your work in the upload submission.  (1 pt) Input the final answer in the given space below. 

Given the following equation (8 pts) Show your work in the upload submission. Input the final answer in the given space below. (1 pt) Use implicit differentiation to find y’.

What is the primary motivation for using the kernel trick in machine learning?

In Kernel PCA, what replaces the sample covariance matrix used in standard PCA, and what does this enable?

In reinforcement learning, the exploration-exploitation tradeoff refers to:

What are required behaviors, actions, or responsibilities that are attached to a specific role?

Is there any evidence or sources that your audience will find particularly credible or trustworthy? Is there any evidence or sources that your audience will doubt or dislike? Make a list of evidence and sources that you may want to use and that you may want to avoid.