Differentiation Questions and Answers

Find the equation of the solution to dy dx x5y through the point x y 1 4 help equations If you round to find the constant please make sure your answers is correct to 3 decimal places

Find the area of the region inside the lima on r 2 cos but outside the circler cos 0 O 40 O 4 3 3 4 20

n 1 how the derivation of and give the Taylor series for cos r around x 2

Rocket Launch A toy rocket is launched straight up in the air from level ground The distance in ft the rocket is above the ground the position function is 170r 161 at any time 1 in sec Find a f 0 b The initial velocity of the rocket FEMME 244

Let F t yz xz xy Find a function fR 3 R such that F gradient f

Sketch a graph of f x 2x 3 4 5 4 3 2 1 5 4 3 2 1 Clear All Draw 1 2 3 5 1 2 3 4 5

Sketch the graph of one function that satisfies all the following conditions lim f x 2 lim f x 2 limf x 1 lim f x 3 lim f x 0 lim f x a x118 x 4 X 0 x 0 x 2 Upload an image or PDF of your solution

Use NDER on a calculator to find the numerical derivative of the function at the specified point 1 2x f x 2x NDER f 2 at x 2

Find the most general antiderivative Use C for the constant of integration Remember to use absolute values where appropriate f x 6x58x 9 f x

4 Explain the relationship between elasticity and revenue maximization The demand for a product is given by p 90 10q Find the elasticity of demand when p 50 If this

In how many ways can a group of five players on the girls basketball team be chosen from a team of 15 players ways

1 10 Pts Compute the directional derivative of the function f x y exy at the point P 0 1 in the direction 2 1

5 10 Pts Consider the function f x y x xy 2y x 4y a Find the critical point s of f x y

a ve b say lar n n aritmetik ortalamas 5 a ve x say la r n n geometrik ortalamas 3 b ve x say lar n n geomet rik ortalamas 11 oldu una g re x ka t r A 1 B 2 C 3 D 4 E 5

Given the following equation of a parabola X O x 2 O x 4 x 2 O x 1 parabola x y 2 y 2 Identify the directrix

Step 2 of 4 Identify the shape of the more basic function found in step 1 Answer 2 Points Ay Cartesian Graph g x x 2 X x x X

a If F x G x then F x G x TRUE

2 Find the first 4 terms and the eighth term of the recursively defined sequence a u 3 and uk 1 uk 10 fork 1 b c 2 c 1 and cx 2 Ck C 1 for k 1

7 The first row of seating in section J of the Athena Arena has 7 seats In all there are 25 rows of seats in section J each row containing two more seats than the row preceding it How many s are in section J

Scores on a certain intelligence test for children between ages 13 and 15 years are approximately normally distributed with 101 and o 27 a What proportion of children aged 13 to 15 years old have scores on this test above 91 NOTE Please enter your answer in decimal form For example 45 23 should be entered as 0 4523 Answer b Enter the score which marks the lowest 20 percent of the distribution Answer c Enter the score which marks the highest 10 percent of the distribution Answer

42 Given a 60 B 42 C 58 What is the area of triangle ABC A 1400 B 2250 C 1040 D 1010

Use the following distribution to complete parts a through d below 3 5 9 12 11 a Compute the mean and standard deviation of the distribution The mean is 8 The standard deviation is 3 87 Round to the nearest hundredth as needed SCULTY b Multiply each number in the distribution by 3 and compute the mean and the standard deviation of this ne distribution The mean is

6 10 5 The real rate of return on an investment is the annual rate of return after taking into account the impacts of inflation It more accurately reflects the purchasing power of your money You can calculate it using the formula below where nominal rate is the given rate of return 1 Nominal Rate 1 Inflation Rate a What is the real rate of return on Hadley s investments Refer back to question 4 Real Rate of Return b What is the real rate of return on Hadley s savings C 1 How does the graph show the impact of inflation on the value of Hadley s savings over time d Question 4 used the equations y 300 1 05 and y 300 1 01 to represent Hadley s savings and investment balances over time respectively Rewrite these equations to represent their account balances based on their real rate of return

Find the derivative of the function 7 g x g x 7 arccos

Find the derivative of the function e6x e6x 9 y y

Use logarithmic differentiation to find dy dx y x6 x dy dx

Solve the equation accurate to three decimal places 1 0 10 365t 365 8

Solve for x accurate to three decimal places Enter your answers as a comma separated list X ex 98

Describe the conic Complete parts a through d r 4 3 4 sin 0 b State whether the directrix is vertical or horizontal O vertical O horizontal Give its location in relation to the pole O A above OB below O c left D right c Find the vertex or vertices Type an ordered pair Type an exact answer using it as needed Use integers or fractions for any numbers d Graph the equation Which of the following is the correct graph for the conic

1 Estimate the area under the curve a Lo Ax b a7 3 0 20 b f x 2x 3 46 1 2 FG 0 5 f f 1 5 f 2 f z 5 16 2 2 3 4 5 6 7 3 2 2 16 5 from 0 3 by finding 5442 123 IN 0 0 5 1 1 5 2 2 5 3

22 25 Find the logarithm of log 9 without using a calculato 7 and f 2 5 what is the value of b

mive the word problem below 24 While floating his kayak David went north down a stream that was 100 feet wide However due to the strong wind blowing east he ended up traveling 160 feet to cross the stream Based on this information how far cast did the wind blow his kayak Estimate your answer to the nearest whole number

A child is 37 4 inches tall The population of children of the same age and gender have a mean height of 39 2 inches with a standard deviation of 6 6 inches Another child is 38 6 inches tall The population of children of the same age and gender as this child have a mean height of 40 5 inches with a standard deviation of 3 5 inches a Which child is taller this is not a trick question no statistics involved here O child 2 O child 1 b What is the z score associated with the height of child 1 Round final answer to two decimal places c What is the z score associated with the height of child 2 Round final answer to two decimal places d Which child is taller relative to their corresponding populations Now you have to use statistics O child 1 Ochild 2

g x Xs n g x x Find g lo xsin 2

Pharmaceutical Theft Pharmaceutical theft has been rising rapidly in recent years Experts believe that pharmaceuticals are the new street gold The value of stolen dru year from 2007 through 2009 is approximated by the function f t 20 5e0 74t 1 t 3 where t is the number of years since 2007 Find the rate of change of the value of stolen drugs at t 1 Round your answer to two decimal places million per year

was signed in 1997 required countries to start reducing their carbon dioxide emissions The protocol became enforceable in February 2005 In 2004 the mean carbon dioxide emission wa 4 87 metric tons per capita Assume the table below contains carbon dioxide emissions from a random sample of countries from a study last year Compute a 93 confidence interval to estimate the mean carbon dioxide emission for all countries last year carbon dioxide emissions in metric tons per capita 1 35 7 84 2 27 0 28 2 45 2 26 0 78 0 79 0 2 2 44 1 45 4 56 5 93 5 36 5 86 7 93 3 46 0 06 2 62 5 85 1 36 1 46 6 72 3 45 1 8 3 02 6 02 2 87 5 94 0 14 2 86 9 11 2 45

Question 9 5 points The graphs of functions f and g are shown below g x f x 2 1 Let u x f g x Find u 1 Y 1 2 3 4 5 6 7 5 H 3 2 1 X

Use the information about the matrices below to determine if the given products are defined Matrix A is a 3x7 matrix Matrix B is a 7x2 matrix Matrix C is a 2x3 matrix Matrix D is a 3x2 matrix Matrix Product A B B A Defined Yes or No Select Select C A Select C D Select A C Select

Assume 5 3 2 h x x x and g 3 5 Find 3

15 Given a rectangular box with length x the height is 2x with length 3x Express the surface area S in terms of its volume V Approximate the change in surface area S as the volume V shrinks from 750 m to 749 m

Chandler the owner of a boutique kept track of which sizes were worn by the store s customers small 3 medium 32 large 22 What is the experimental probability that the next customer to come into Chandler s boutique wears a size small Simplify your answer and write it as a fraction or whole number P small

2 Assume y y x a function of x find dy dx if exy In x y

8 Select a function y f x x and dx and find dy to approximate 1001 1 3

Evaluate the following limit lim 7x 1 3cotx X 0 O lim 7x 1 3cotx 3 vint O O lim 7x 1 3cotx e21 vant lim 7x 1 3cotx 21 vint O lim 7x 1 3cotx e3 vint

5 Find the inflection point s for the function f x 10x 2x 3 O 0 3 and 1 15 O 1 15 O 0 3 O 1 10

Write the equation of the line tangent to f x O y 6x 7 O y 6x 2 O y 1 Oy 6x 7 5 6 1 6 xo when x 1

Evaluate the difference quotient for f x O O O O 1 x h 9 7 x h 9 x 9 7 x h 9 x 9 1 x h 9 x 9 7 x 9

Use logarithm properties to write 12log2y 7log w 15log z as a single logarithm O log 2 w z 5 W y 1092 1276 15 O log log 28yw log z 5 O log 28 O

Let f x x 7x on 4 9 Use the IVT to determine if there is a solution to f x 10 in the interval between 4 and 9 If so find the value of c in the interval such that f c 10 O O f x is continuous on 4 9 10 is between f 4 12 and f 9 18 c 2 c 5 f x is continuous on 4 9 10 is between f 4 12 and f 9 18 c 5 f x is continuous on 4 9 10 is between f 4 12 and f 9 18 c 2 f x is continuous on 4 9 10 is not between 4 and 9 so the IVT does not apply

Given 7x ex 6y 12 compute dx O O O 21x 12 dx 18y ye 1 dx dy dx dy 21x 18y yev 1 21x 12 18y ex 21x 1