Question

Revised by Prof. Kostadinov, Fall 2015, Fall 2014, Fall 2013, Fall 2012, Fall 2011, Fall 2010 Revised by Prof. Africk and Prof. Kostadinov Fall 2015, Spring 2016, #1 Identify the horizontal and vertical asymptotes of the following functions using the limit definitions: 2x2 o) yA- #2 Find the derivatives of the following functions using the definition of derivative: a) f(x)-2x-5x #3 Find the derivative v dr of the following functions, using the derivative rules: b) f(x)--2x +3x-4 #4 Find the derivatives of the following functions 2x2 4x2-5 2x-1 x-16 dr of the following functions using logarithmic differentiation: #5 Find the derivative y Find the equation of the tangent line, in slope-intercept form, to the curve: a) f(x)-2x' +5x +6 at (-1,9) #6 b) f(x)-4x-x at 1,3) #7 using implicit differentiation, find the equation of the tangent line to the given curve at the given point: a) 3ry-3y-17-5x+14 at ,-3) b) y-xy+-2r-9 at (0,3) Eat x 27, Round your #8 Use differentials to approximate /273 using the value of the function y-f(x)- answer to the nearest thousandth. #9 wire of length 20m is divided into two pieces and the pieces are bent into a square and a circle. How should this be done in order to minimize the sum of their areas? Round your answer to the nearest hundredth. #9 wire of length 20m is divided into two pieces and the pieces are bent into a square and a circle. How should this be done in order to minimize the sum of their areas? Round your answer to the nearest hundredth. #10 Find the dimensions of a closed box having a square base with surface area 12 and maximal volume. #11 If a snowball melts so its surface area decreases at a rate of 1 cm2/min, find the rate at which the diameter decreases when the diameter is 6 cm. #12 The radius of a sphere increases at a rate of 3 in/sec. How fast is the volume increasing when the diameter is 24m? #13 The radius of a cone is increasing at a rate of 3 inches/sec, and the height of the cone is 3 times the radius. Find the rate of change for the volume of that cone when the radius is 7 inches #14 Sand pours from a chute and forms a conical pile whose height is always equal to its base diameter. The height of the pile increases at a rate of 5 feet/hour. Find the rate of change of the volume of the sand in the conical pile, when the height of the pile is 4 feet #15 A cylindrical tank with radius 8 m is being filled with water at a rate of 2 m3/min. What is the rate of change of the water height in this tank? #9 wire of length 20m is divided into two pieces and the pieces are bent into a square and a circle. How should this be done in order to minimize the sum of their areas? Round your answer to the nearest hundredth. #10 Find the dimensions of a closed box having a square base with surface area 12 and maximal volume. #11 If a snowball melts so its surface area decreases at a rate of 1 cm2/min, find the rate at which the diameter decreases when the diameter is 6 cm. #12 The radius of a sphere increases at a rate of 3 in/sec. How fast is the volume increasing when the diameter is 24m? #13 The radius of a cone is increasing at a rate of 3 inches/sec, and the height of the cone is 3 times the radius. Find the rate of change for the volume of that cone when the radius is 7 inches #14 Sand pours from a chute and forms a conical pile whose height is always equal to its base diameter. The height of the pile increases at a rate of 5 feet/hour. Find the rate of change of the volume of the sand in the conical pile, when the height of the pile is 4 feet #15 A cylindrical tank with radius 8 m is being filled with water at a rate of 2 m 3/min. What is the rate of change of the water height in this tank? #16 A box with a square base and an open top must have a volume of 256 cubic ınches Find the dimensions of the box that will minimize the amount of material used (the surface area) #17 A farmer wishes to enclose a rectangular plot usina 200 m of fencing material. One side of the land borders a river and does not need fencing. What is the largest area that can be enclosed? x3-3x2-1, use the first and second derivative tests to: #18 For the function y (a) determine the intervals of increase and decrease. (b) determine the local (relative) maxima and minima (c) determine the intervals of concavity (d) determine the points of inflection. (e) sketch the graph with the above information indicated on the graph #19 Sketch the graphs of the following functions. Find and label any intercepts and horizontal and vertical asymptotes 2x2 b) 4 2-4

Answer 1

③@) Findihiq dni vaj:ved hう。 h-90 hyo 万

-42+3 dt dt du dau d b x sinx.

(Sinu dx χ.dnCidin) + Coi 3xda (n) 프(Xan5X) ะ 1xt dy da -계 ly