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Math 120: Assignment 3 (Due Tues., Sep. 25 at start of class) Suggested practice problems (from Adams, 6th ed.): 2.1: 2.2: 2.3: 2.4: 3,9,15,17,21,23,31 3,5,11,17,23,25,35,39,43,47,49,53 1,5,9,15,25,29,31,33,43,47 1,13,15,25,29,33,35,39 Problems to hand in: 1. At which points x is the function f (x) = (4 − x2/5 )−5/2 differentiable? Compute its derivative. 2. At which points t is the function f (t) = tive. √ 2 √1+t −1 1+t2 +1 3. Let f and g be differentiable functions. Find and g 0 . 4. Compute d −2 dx x d dx differentiable? Compute its deriva- f (g(xf (x)))2 in terms of f , g, f 0 , using the definition of the derivative. 5. Find an equation for the tangent line to the graph y = 6. Show that the graphs y = x2 and y = √1 x x2 +3 √ x1/3 + x at x = 1. intersect at right angles. 7. Consider the functions f1 , f2 , and f3 , defined by ( j x x 6= 0 |x| fj (x) := 0 x = 0, j = 1, 2, 3. Which of them are continuous at x = 0? Which of them are differentiable at x = 0? 1