1) If you pluck a guitar string, pulling it to a height of A and letting go, we can model its motion as f(t) = A cos(t), where t is in milliseconds and A is a constant. a. The derivative tells you how fast the string is moving, and thus how loud the sound will be. Find the derivative. b. The faster it moves (bigger derivative), the louder it will be. What is the relationship between how far you pluck the string, A, and how loud it is? c. What is wrong with our model as t gets big (as compared to what you expect from a real guitar string).

sol only thank you.

9. Fill in the blanks AND give reasons for each step of the calculation. Let y = arctan(r+ e). (This could also be written y = tan- (r + e).) We will find its derivative. First rewrite the equation as tan( using the definition of Now apply the method of to get 윤 tan( On the left side of the equation we use the to get: sec ( Now we solve for to get = This shows that arctan(r+ e") %3D If we want to, we can use trigonometry to write the final answer using only the variable r, but for simplicity we'll leave the answer as it is.