Test 2 Practice Problem 1. Find the following derivatives (you do NOT need to simplify). (a) a 4 cos (3x) dx (b) da a 31 + 23 + 3x +3 (c) - 2 5 tan-1 (4) dx (d) 7 sin -1 (2x + 4) d x 2 csc -1 (x ) (e) dx d ( f) dx d tan(x) + 1 dx - 4 (h ) d dx - sec(sin(22) + cos-1(x)) 12 (i) - xtan(2) 10g3 ( 2 2 + 1 ) (j) dx (k) - (x In x - x) d dx - In(sin(x)) Problem 2. Evaluate the following limits, making sure to show all work. tan (5x) a lim I-+0 6x sin (x - 1) (b) lim 3x - 3 sin (5x) (c lim I -+ 0 2x Problem 3. Find the equation of the tangent line to the following equation at (0, 0): cot -1(y) + tan -1(x) = (y - 1)x+ 5.Alt Alt Problem 4. Solve for dx dy given sin(y) = ety + sec2 (x) . Problem 5. Find the second derivative of cot(x). Problem 6. If f(2) = 4, 9(2) = 1, f'(2) = -1, g'(2) = -2, find h'(2) where h(x) = f(19(x)). Problem 7. For what values of t is h(t) = Vt - 2 NOT differentiable? Problem 8. Use logarithmic differentiation to find the derivative of ( + 5) tan?(x) $/x2 + 5x Problem 9. As a little girl is riding her bike home and bringing her balloon along with her, she accidentally lets go of the balloon at it starts to float straight up at 3 ft/sec. The little girl continues riding her bike at about 8 ft/sec in a straight line. When she is 30 ft past where she released the balloon, how fast is the distance between them changing? 2