Differentiation Questions and Answers
Calculus
Differentiationous at r a Illustrate each case with a picture 9 How can a function f x fail to be differentiable at a number 1 illustrate each case with a picture 10 Give the accurate definition of a concave upward and a each case with CORS Explain a Explain all cases and
Calculus
DifferentiationUse implicit differentiation to find dy dx and d y dx x3 5 y3 5 8 O dy y2 5 d2y x2 5 dx2 O F O dy y2 5 d2y x2 5 dx2 y2 5 d2y x2 5 dx2 dy x2 5 d y dx y2 5 dx2 2y1 5 2x T 5x7 5 3 5 2x3 5 273 5 5x7 5 1 5 2x3 5 2y3 5 5x7 5 1 5 2x3 5 2y3 5 5x1 5 7 5
Calculus
DifferentiationBoyle s law states that the volume of a gas varies inversely with applied pressure Suppose the pressure on 60 cubic meters of gas is raised from 1 atmosphere to 3 atmospheres What new volume does the gas occupy cubic meters
Calculus
DifferentiationSuppose that a y 82 dy 1 Use the method of implicit differentiation to find da dy dx x3 2 Find the equation of the tangent line at the point x y 3 1 The equation is X 27x80
Calculus
DifferentiationThe curvature of the helix r t a cost i a sin t j bt k a b20 is x The largest value x can have for a given value of b is a a What is the largest value x can have for a given value of b www
Calculus
DifferentiationFind T N and x for the plane curve r t 4cost 4t sin t i 4sin t 4t cos t j t 0
Calculus
DifferentiationL et et dt Find an equation of the tangent line to the curve y x at the point with x coordinate 3 Let F x
Calculus
Differentiation15 Find an equation of the tangent line to the graph of the function f x x 3x 3 3 3 at the point a y 6 b y 3x 6 c y 9x d y 3x e y 9x 24
Calculus
Differentiation14 Find the derivative of the function a b c d le 5 2 5x 2 5 2 5x 2 5x 5x 2 5 x 5x 2 f x f x f x f x 5 5x 2 f x 5x 2
Calculus
DifferentiationEstimate the area of the region bounded by the x axis and the graph of y sin x from x 0 to x 3 using six rectangles and using right endpoints Draw the region and show your six rectangles Write your solution on paper and upload an image of a PDF file of your solution
Calculus
DifferentiationThe tangent line to a smooth curve r t f t l g t h t k at t to is the line that passes through the point to 9 to h t parallel to v to the curve s velocity vector at to User to and r to to find parametric equations for the line that is tangent to the given curve at the given parameter value t to r t cos t i 3 sin t j 3 k o 0 Find the standard parametrization for the tangent line OA x 1 y 3t z 3 9t OB x 1 y 2t 3 z 3 c x 0 y 3t z 3 9t D x 0 y 2t 3 z 3 CIES
Calculus
Differentiationear total active iPhones in US in millions of units 8 17 24 40 51 72 88 101 114 125 127 131 138 141 149 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 total active iPhones in US in millions of units vs year 7 17 11 8x 2 12x 2 0 0578x 3 total active iPhones in US in millions of units 150 100 50 0 8 10 12 14 year 16 18 20 22
Calculus
DifferentiationGiven the table of values below find the average rate of change of the function f x on the interval 5 13 4 9 70 162 X f x 5 94 6 102 7 123 8 141 10 195 11 199 12 232 13 238 14 251
Calculus
DifferentiationAugustus bor 2 In the subtraction below a b and c are digits and a is less than 6 What is the value of e ba ab cfi
Calculus
Differentiation37 Aidan and his sister Ella are having a race Aidan runs at a rate of 10 feet at a rate of 6 feet per second Since Ella is younger Aidan is letting her begin 30 feet ahead of second Ella runs per the starting line Let y represent the distance from the starting line and x represent the time elapsed in seconds Write an equation to model the distance Aidan traveled Write an equation to model the distance Ella traveled
Calculus
Differentiation1 x If x 0 2x 1 If x 0 Let f x Evaluate f 7 and 2 f 7 f 2 If you have had difficulty with these problems you should look at Sections 1 1 1 3 of yo
Calculus
DifferentiationRewrite by completing the square 2x 4x 11 If you have had difficulty with this problem you may wish to cons
Calculus
DifferentiationExpand and simplify 2 x 6 3 4x 5 If you have had difficulty with this problem you may wish t
Calculus
DifferentiationAnswering calcPad Questions VebAssign calcPad questions are displayed with a rectangular answer box similar to answer boxes used for other question types but when you click a calcPad enabled answer box the calcPad pa pens allowing you to answer the question with a correctly formatted mathematical expression This exercise requires you to enter a mathematical expression Your answer should be To enter this answer 1 Click the answer box to open the calcPad palette VO 2 Click in the palette
Calculus
Differentiationmathematics expressions are case sensitive 3x is not the same as 3X WebAssign follows these rules his exercise requires you to enter a mathematical expression Enter D P To enter this answer 1 Click the answer box to open the calcPad palette 2 Type D p pi 3 Notice that the word pi has automatically changed to the symbol 4 Submit your answer
Calculus
DifferentiationFind the first five terms ao a1 02 03 04 in the series solution at z 0 of the initi value problem IVP x 1 y xy y 0 y 0 0 y 0 1
Calculus
DifferentiationDetermine the equation of the line passing through the points 1 1 and 1 7 Write the line in standard form Ax By C
Calculus
DifferentiationLet f x y 5x xy e evaluate f 4 3 f 3 0 2 Let g x y 0 25x 3x y find the followin partial derivatives A gx B gy
Calculus
Differentiation3 Let z 800 62xy 15y evaluate dz A 2 1 dx B z 2 3 4 Let R x y 0 1x y4 5x 6y find the secon partial derivatives A B 8 R dy a R a ar oxdy dx dy
Calculus
DifferentiationTHE nd the equation of the linear function whose graph is given here Use the letter X ultiplication symbol 654321 7 6 5 4 3 2 1 21 4567 LLLL 1 2 3 4 5 6 7 Son 1
Calculus
DifferentiationFind the equation of the line passing through the points 7 7 and 7 5 Your answer should take the form x aor y a whichever is appropriate
Calculus
DifferentiationAlden Company s monthly data for the past year follow Management wants to use these data to predict future variable and fixed costs Month Units Sold 320 000 160 000 2 Units Income 280 000 200 000 300 000 200 000 Total Cost 160 000 100 000 220 000 100 000 230 000 120 000 Contribution margin Fixed costs Income Predictions 220 000 0 Month 7 8 b 9 2 Predict future total costs when sales volume is a 220 000 units and b 240 000 units 10 11 12 240 000 Units Sold 340 000 280 000 80 000 0 160 000 100 000 110 000 Total Cost 220 000 160 000 64 000 140 000 100 000 80 000
Calculus
DifferentiationFrom the table below we can conclude that the function f has a local maximum at x f x 3 6
Calculus
DifferentiationRewrite the integral in terms of k dv Step 3 H K V Let u xe Substitute the value of k du 1 C 1 N 7 7x 1 2 7 k dk xe7x Differentiate u with respect to x Jx dx xe7x e dk 7 1
Calculus
Differentiation64 64 1 1 sin x Step 4 Recall the Pythagorean identities which state that sin u cos u 1 1 tan u sec u 1 cot2 u csc u Use the appropriate Pythagorean identity Therefore the expression simplifies to
Calculus
DifferentiationFind the derivative f x x 2x 4 8x 16 A f x 1 33x 2 4x 1 2 8 OB f x 3x 2 4x 1 2 8 OC f x 3x 2 2x 1 2 8 2x 1 2 OD f x 1 33x 1 33x1 2 8
Calculus
DifferentiationAssume that a demand equation is given by x 7000 100p Find the marginal revenue for the given production levels values of x Hint Solve the demand equation for p and use R x xp a 2000 units b 3500 units c 4500 units a Choose and fill in the correct response for x 2000 OA The marginal revenue at 2000 units is per production level OB The marginal revenue at units is 2000 production levels per 1 units is 2000 per production level OC The marginal revenue at OD The marginal revenue at 2000 units is production levels per 1 b Choose and fill in the correct response for x 3500 OA The marginal revenue at OB The marginal revenue at 3500 units is OC The marginal revenue at units is 3500 OD The marginal revenue at 3500 units is c Choose and fill in the correct response for x 4500 units is 3500 per production level production levels per 1 production levels per 1 per production level OA The marginal revenue at 4500 units is per production level GELER