MATH 7, EXAM#2 Name Instructions. Write your answers on the provided answer sheet. 9 points will be given for the correct answers. ZERO to FOUR points will be given for the wrong answers. No points will be given if only an answer is indicated. ' - - = 3- L- 3 L 1. Fmdthe rstderivatlveofx) 3x 4Jf+ J3 6+ W7 2. Use implicit differentiation to find y! for x3 + sin y y2 = 3. Use implicit differentiation to nd y". for x4 + y4 = a4 2 2 4. Find the equation of the tangent line to the graph of 5% E = 1 at (xo,yo). 5. Find the derivative ofy =x) = sin 4x2 + 9 6. A boy is ying a kite that is 20011 above ground. The wind is carrying the kite horizontally away from him at a rate of 20/s. How fast must he let out the string when the kite 40011 away from him? 7. A spherical lollipop is being sucked on by a small child. The lollipop is losing its volume at a rate of 600mm3/min. How fast will the radius be decreasing when the radius of the lollipop is 10mm. 8. Use a linear approximation ( or differentials) to estimate m .(show work) 9. The position ofa particle is given by the equation .9 =t) = r3 9:2 + 24! 3. Find the velocity aer two seconds. I). When is the particle at rest? c. When is the particle moving forward (positive direction)? d. Draw a diagram to represent the motion of the particle? e. Find the total distance traveled by the particle during the rst five seconds. 1'. Find the acceleration at time t and after 4 seconds. 32:, ifx 1 Find the unique values for a and b that will make f both continuous and ax + x r x _ 10. Given fix) = { differentiable. 11. Find lim SEW'1) x4] I +x2