Differentiation Questions and Answers

Compute the following 2x x 7x 3 dx 2x x 7x 3 1x 2 lx 2 Simplify your and

the first and second derivati y 4x 1 4 01

Find the following f x x 2 g x x 2 a f g x b f g x c fg x d f g x What is the domain of f g Enter your answer using interval notation

For the function f x 9x x make a table of slopes of secant lines and make a conjecture about the slope of t tangent line at x 1 Complete the table Round the final answer to three decimal places as needed Round all intermediate values to four decimal place needed Interval 1 2 1 1 5 1 1 1 1 1 01 1 1 001 Slope of secant line 62 41 75 28 79 26 27 26 An accurate conjecture for the slope of the tangent line at x 1 is Round to the nearest integer as needed

e function f x 9x x make a table of slopes of secant lines and make a conjecture about the slope ant line at x 1 plete the table nd the final answer to three decimal places as needed Round all intermediate values to four decimal pl ed Interval 1 2 Slope of secant line

The path r t t i 212 9 j describes motion on the parabola y 2x2 9 Find the particle s velocity and acceleration vectors at t 1 and sketch them as vectors on the curve CIUD The velocity vector at t 1 is v 1 i j Simplify your answer including any radicals Use integers or fractions for any numbers in the expression

The tangent line to a smooth curve r t f t i g t j h t k at t to is the line that passes through the point f to 9 to h to parallel to v to the curve s velocity vector at to Use r 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 4 sin t i t 6 cos t j 4e4t k to 0 What is the standard parametrization for the tangent line X y Z Type expressions using t as the variable

4 Explain how to use the unit circle to evaluate a trig ratio for an angle with negative measure 2 T For example sin 45 or cos 3

6 Which of the following has a negative value 57 4 A tan B sin D COS 57 4 COS 47 3 13TT 6

Evaluate tan 55 3

Problem 1 Evaluate the following integrals a 4x 3 dx Sx 2 x4 dx b c d 1 Sxx dx x 1 ln x S dx x 1

Suppose a sphere of radius r is sliced by two horizontal planes h units apart as shown Show that the surface area of the resulting zone on the sphere is 2xrh independent of the location of the cutting planes To show that the surface area of the resulting zone of the sphere is 2xrh independent of the location of the cutting planes find the surface area of the zone Orient the sphere so that the planes are vertical as shown in the figure This allows the computations to be done in terms of x Let r represent the radius of the sphere in the problem statement Write the equation of the curve that when revolved about the x axis on the interval r r will result in the sphere given in the problem statement f x

The volume of a swimming pool is 2080 cubic feet Assuming that the pool is 16 feet long and 10 feet deep find its width The width is

Differentiate the function in two ways f x 2x 2x 3 a Use the general power rule b Multiply 2x2 2x 3 by itself and then differentiate the resulting polynomial a Rewrite f x using the general power rule 0 1 f x

Suppose f 5 8 f 5 4 g 5 5 and g 5 6 Find h 5 and h 5 where h x 5f x 2g x h 5 Simplify your answer

Differentiate dy dx 4 y 16 4x 4

Differentiate 2 y 3x 2 dx 3x 11

Differentiate d dx y 3x 2 5 3x 2 5

Differentiate dy dx y 7 3 6x

e number 2 511863 rounded to 2 significant figures is e number 553 7165 rounded to 4 significant figures is e number 25 58464 rounded to 3 significant figures is Submit Answer Retry Entire Group 9 more group atter

ften necessary to do calculations using scientific notation when working chemistry proble rm each of the following calculations x 105 2 31 x 10 x 10 5 9 48 x 105 3 36 x 104 7 00 10 5 X 05 2 3 18 x 105 mit Answer 10 2 31 10 Retry Entire Group 9 more group attempts remaining

thermometer reads 32 1 C Calculate this temperature in Fahrenheit degr ahrenheit temperature Submit Answer Retry Entire Group F 9 more group attempts remaining

63 43 0 08852 177 24 0 823958 Submit Answer Retry Entire Group 8 more e proup attempts remaining

Determine the open intervals on which the function is increasing decreasing or constant Enter your answers using interv notation If an answer does not exist enter DNE f x x 2x increasing decreasing constant f x 0 f x 0 DNE 2 1 X X y 8 9 4 2 1 2 3 4 X

Maintenance money for an athletic complex has been sought Mr Kendall the Athletic Director would like to solicit donation to cover all future expected maintenance costs for the building These maintenance costs are expected to 1 5 million each year for the first five years 1 8 million each year for years 6 through 10 and 2 million each yea after that The building has an indefinite service life If the money is placed in an account that will pay 8 interest compounded annually how large should the gift be Click the icon to view the interest factors for discrete compounding when i 8 per year The gift should be S million Round to two decimal plagos

Add and subtract as indicated 1 37 45 26 24 3 51 55 37 45 5 61 33 45 16 7 90 34 12 9 180 120 17 11 76 24 13 70 40 22 34 30 50

Is the graphed function differentiable at x 3 Choose the correct answer below OA Yes because f x has a non vertical tangent line at x 3 OB No because the tangent line to f x at x 3 is vertical OC Yes because f x has two tangent lines at x 3 both non vertical Next question C 10 8 6 4 2

17 18 19 and 20 Verify that the function satisfies the hypotheses of the Mean Value Theorem on the given interval Find all numbers c that satisfy the conclusion of the Mean Value Theorem 17 f x 2x 3x 1 0 2 18 f x x 3x 2 2 2 19 f x lnx 1 4 1 20 f x 1 3

Is the graphed function differentiable at x 5 Choose the correct answer below OA Yes the function is differentiable at x 5 OB No because while the function is continuous at x 5 it has a vertical tangent line at x 5 OC No because while the function is continuous at x 5 it does not have a tangent line at x 5 OD No because the function is not defined at x 5 OE No because while the function is defined at x lim does not exist X 5 OE No because while the function is defined at x 5 and lim exists lim is not equal to the value of the function at x 5

function graphed is of the form ya sin bx or ya cos bx where b 0 Determine equation of the graph 1 5 3 1 1 3 A

Determine the amplitude and period of the given function Graph the function 2 X y 3 sin The amplitude is Simplify your answer Type an exact answer using it as needed

4 3 Points DETAILS SCALCET9 2 XP 8 003 Trace or copy the graph of the given function f Assume that the axes have equal scales Use estimates of the derivative off to skatch the graph of on the same coordinate axes 8 00 Do 20

6 3 Points DETAILS SCALCET9 2 XP 8 006 Trace or copy the graph of the given function f Assume that the axes have equal scales Use estimates y the derivative off to sketch the graph of f on the same coordinate axes

dentify the line that has each slope Li a m 0 0 41 042 OL3 b m 3 4 O 41 0 42 OL3 c m 1 0 41 042 L3 L

below A B C owing questions about the function f whose graph is show graph of the function f Find lim f x 2 Find lim Find lim h 0 0 h f 0 1 does h 2 h Find lim f x undhud x 0

The displacement in feet of a particle moving in a straight line is given by s 12 9t 16 where t is measured in seconds a Find the average velocity in ft s over each time interval 1 4 8 3 6 8 2 8 10 0 iv 8 12 20 10 10 ft s b Find the instantaneous velocity in ft s when t 8 1 ft s c Draw the graph of s as a function of t and draw the secant lines whose slopes are the average velocities in part a Then select the graph of s with the tar 20 ft s 10 EM 10 15 10 15 20 30 ft s X ft s Do 10 15 10 5 5 10 15 20

f a h f a h h 0 3 Use the definition of the derivative f a lim to compute f 3 for the following functions Then match the functions with their graphs shown below using your limit results a f x x 3 2 b f x x 3 2 c f x x 3 2

14 A sign is hanging from a storefront The two ropes holding it are fixed at angles of 25 and 35 with the horizontal If the sign has a weight of 1150 N what is the tension in each rope A 3 T 2

Find the volume of the solid generated by revolving the region R bounded by y ex y 0 x 0 and x In 3 about the x axis Set up the integral that gives the volume of the solid In 3 z e 2x dx Type exact answers The volume of the resulting solid is cubic units

Find the vertical asymptote x L f x 4 2 x 1

Find the horizontal asymptote y Ny 2 1 x 5 x 3x 2

Use limits to compute f x f x 1 13x

Suppose that lim f x 9 and lim g x 3 Compute the limits that exist X 4 X 4 a lim f x 3g x X 4 b lim f x g x X 4 A c lim 4f x g x X 4 a Select the correct choice below and if necessary fill in the answer box to complete your choice lim f x 3g x 0 x 4 Type an integer or a simplified fraction B The limit lim f x 3g x does not exist X 4 d lim X 4 f x f x g x OB The limit lim f x g x does not exist X 4 b Select the correct choice below and if necessary fill in the answer box to complete your choice OA lim f x g x X 4 Type an integer or a simplified fraction

Question Determine the area in square units of the region bounded by g x 7x 7 and f x x 11x 28 over the inter 3 7 incorrect Truagain

1 point Find the derivative of the function G x G x 5 cost dt

The graph on the right gives the annual per person retail availability of beef chicken and pork in pounds from 2007 to 2012 What is the approximate annual per person retail availability of beef chicken and pork in 2012 The annual per person availability of beef in 2012 is approximately Pounds 70 65 60 55 50 45 efettalicates 40 35 2007 2008 2009 2010 2011 2012 Year pounds

Simplify 2 4 2 11 1 16 Type an in That s incorrect Use the quotient rule of exponents m m n x 0

Use the quadratic formula to solve the equation If the solutions involve square roots give both the exact and approximate solutions 5x 3x 7 0 What are the exact solutions Select the correct choice below and if necessary fill in the answer box to complete your choice OA The solution s do es not involve s square roots The solution s is are x Simplify your answer Use a comma to separate answers as needed OB The solution s involve s square roots The solution s is are x Type an exact answer using radicals as needed Use a comma to separate answers as needed OC There are no real solutions

Answer Formats f x 2x 15x 84x 12 x If the function does not have any enter NONE If the function has more than one type your answer as a comma separated list For example m

Oil leaked from a tank at a rate of r t liters per hour The rate decreased as time passed and values of the rate at two hour time intervals are shown in the table In this problem we are going to estimate the total amount of oil that leaked out during this ten hour time period t hours 0 2 4 6 8 10 r t L hr 9 4 7 7 7 3 5 9 4 8 4 1 Rate of Oil Leakage Left Endpoint Approximation Estimate the total amount of oil that leaked out using left endpoints Total Amount of Oil Right Endpoint Approximation Estimate the total amount of oil that leaked out using right endpoints Total Amount of Oil liters liters