Application of derivatives Questions and Answers

Recall that 180 corresponds to radians Convert the degree measure given to radian measure in terms of t 18 18 radians Type an exact answer in terms of

Use derivatives to determine whether f is increasing or decreasing on the given interval Use L4 or R4 whichever is appropriate to give an overestimate of the signed area on the given interval f x 9e on 0 1 get Is the function increasing or decreasing over the interval OA The function is decreasing because f x 0 over the interval OB The function is increasing because f x 0 over the interval OC The function is decreasing because f x 0 over the interval O D The function is increasing because f x 0 over the interval

Calculate 7x dx given the following 9 9 x dx 728 x ax 271 xd dx fxdx 3 3 1 1 1 7x dx 10 10 7x 1 Type an integer or a simplified fraction 9 xdx 40

Calculate 5 5x dx dx given the following 8 4 5 61 Sxdx 4 5 Sx dx 01 3 4 8 x d X 5 dx 129 5 5x dx 8 Type an integer or a simplified fraction

Calculate J 4x dx given the following 3 9 Sx dx 3 dx 36 9 4x dx 8 Sx dx 3 485 3 9 x dx 8 217 3

A particle is moving with acceleration given by a t 6t 12 and an initial velocity of 9 m s a Find the velocity of the particle at time t b Find the velocity of the particle after 3 seconds c When is the particle at rest d When is the particle moving in the positive direction e Find the total displacement of the particle during the first 8 seconds

Calculate the definite integral by referring to the figure with the indicated areas Area A 1 213 Area B 2 539 0 f x dx Area C 5 777 Area D 1 672 COL Ab a B

Graph the region R bounded by the graphs of the indicated equations Describe R in set notation with double inequalities and evaluate the indicated integral y 1 x y 1 x x 1 6x y 11 da Select the correct graph below 1 O A Ay 6 FR X Q R OB Ay F Q O C Ay 6 6 X Q Q Q O D Ay 6 6 X

Evaluate the integral Graph the region of integration reverse the order of integration and then evaluate the integral with the order reversed 1 2 x SS 0 2x Evaluate the integral 12 x S S 0 2x x dy dx O A x dy dx Graph the region of integration Choose the correct answer below Ay 2 15 Q Q U OB H Q Q OC Q OD Q n Q 2

Evaluate the following integral Graph the region of integration and then reverse the order of integration and evaluate the integral 6 6 X S S x 6y dy dx 0 0 6 6 x 0 0 x 6y dy dx 252 Simplify your answer Graph the region of integration Choose the correct graph below OA OC ON CCCON OB IN

Find the average rate of change of g x 4x 4 from 4x 4 from x 1 to x 1 1 Enter an integer or decimal number more Quortion Help

Given f x x 9 and g x interval notation Domain of f g x Domain of g f x x 10 determine the following Write each answer using

An angle below the horizontal is called an angle of depression as seen in the figure to the right An airline passenger sees a lake at an angle of depression of 23 If the plane is flying at an altitude of 31 000 feet find the distance from the plane to the lake Which of the following trigonometric ratios should be used to find the unknown distance using the information given in the problem statement A sin 0 OB tan 0 Opposite Hypotenuse OC cos 0 Opposite Adjacent Adjacent Hypotenuse Angle of depression Find the distance The distance is miles Round to the nearest mile as needed

X Use the graph of y ex and transformations to sketch the exponential function f x ex 4 Determine the domain and range Also determine the y intercept and find the equation of the horizontal asymptote Use the graphing tool to graph the function Click to

Use transformations of the graph of f x x to determine the graph of the given function h x x 1 Use the graphing tool to graph the function Click to enlarge graph

A new exhibit hall at a convention center has a floor bounded by x 0 x 200 y 300 0 01x and y 300 0 01x The ceiling lies on the graph of C x y 50 0 15x Each unit on the x y and z axes represents one foot Find the volume of the exhibit hall in cubic feet The volume of the exhibit hall is Simplify your answer cubic feet

Minimize f x y z x y z subject to 6x 2y 8z 104 X 6 y 2 Z 8 The value of f at the minimum is

7 Graph the point with the polar coordinates 3 Choose the correct graph of the point below O A 5 X O B 5 Give two alternative representations of the point in polar coordinates 5 X O C 5 5 X O D 5 5 5

A manufacturing company produces two models of an HDTV per week x units of model A and y units of model B with a cost in dollars given by the following function C x y 6x 12y If it is necessary because of shipping considerations that x y 90 how many of each type of set should be manufactured per week to minimize cost What is the minimum cost To minimize cost the company should produce units of model A

Medical research indicates that the risk of having a car accident increases exponentially as the concentration of alcohol in the blood increases The risk is modeled by R 6e1277 where x is the blood alcoh concentration and R given as a percent is the risk of having a car accident What blood alcohol concentration corresponds to a 17 risk of a car accident Round to 2 decimals when necessary

Minimize f x y x xy y subject to y 20 without using the method of Lagrange multipliers instead solve the constraint for x or y and substitute into f x y Use the constraint to rewrite f x y x xy y as a function of one variable g x g x x 20x 400 The minimum value of f x y x xy y2 subject to y 20 occurs at the point Type an ordered pair

Maximize f x y 10x y subject to x y 2 without using the method of Lagrange multipliers instead solve the constraint for x or y and substitute into f x y Use the constraint to rewrite f x y 10x y as a function of one variable g x g x www

Find f 4 f 3 if possible y f x 4 3 A 2 3 4 5 2 3 5 4 3 2 11 5 THESERIE S

12 Jolene s mother has a job jar that contains 4 slips of paper each with a different household chore written on it One of the chores is washing the dishes Daily chores are assigned by having each family member randomly select a slip of paper from the jar After the chores for the day are assigned all of the slips of paper are placed back into the jar for the next day If Jolene gets to draw first each day what is the probability that she will be assigned to wash the dishes on Monday and Tuesday 3 pts

Let F ayz i ax bz j cx 3y k where a b c E R a Find the values of a b c such that the vector field F is conservative in R b Find a potential function o for the vector field F for values of the parameters a b c that you found in Part a c Consider the line integrals F dr where is the curve formed by the intersection in the first octant oriented of the plane z 3 and the surface z anticlockwise when viewed from above 3x Calculate the line integral i For arbitrary values of the parameters a b and c ii Using the potential function found in Part b i e for the special case of the

Problem 4 5 points A bacteria culture grows with constant relative growth rate The bacteria count was 400 after 2 hours and 15625 after 6 hours Answer the following questions

Step 3 of 3 Identify four ordered pairs on the graph of the function Answer f x 11 x 8

3 0 1 If A 1 5 14 10 7 6 13 A B 69 B 11 2 3 8 7 6 10 35 7 0 and C 14 3A 69 6 9 1 8 2 4 calculate the value of each expression below 15 CB 69

Find the value of each determinant below 8 66 2 5 8 11 9 67 6 3 2 1 11 4 503

5 10 f z dz f x dz f z dx 1 e f t dt 8 5 8 what are the bounds of integration for the first integral a and b

Evaluate by interpreting in terms of areas 3 3 6 2x dx

find the two numbers whose product is 64 and whose sum is minimum

In Problems 15 18 evaluate fe 2x y dx xy dy on the given curve from 1 2 to 2 5 15 y x 3 16 y x 1

Use the graph of the given function f to determine lim f x at the indicated value of a if it exists If an answer does not exist enter DNE 3 X 2 2 1 4 3 2 1 1 a 2 2 X Step 1 For a 2 the limit we must determine from the graph is as follows lim f x Therefore we are looking for the value if it evicts such that u flv can he made as close to as we want if we make y close enough to

credit 1 A truck is driven at a variable rate for 3 hours so that its velocity at any time t 0 t 3 is given by v t 34 12 cos 4t miles per hour How far does the truck travel during the 3 hours

A trail mix contains a mixture of nuts pecans walnuts hazelnuts and peanuts If the probability of reaching into the trail mix and getting pecans is 0 11 what is the probability of not getting pecans Express your answer as a fraction in lowest terms or a decimal rounded to the nearest hundredth Answer 2 Points Keypa

2 Estimate the area of the region above the x axis and under the graph of the function from x 0 to x 5 4 3 2 1 0 0 TS 2 3 4 5 X

Part 1 of 8 The center of the ellipse is Correct Answer The center of the ellipse is 0 0 Part 2 of 8 a 8 b 6 Part 2 8 Part 3 of 8 28 0 The vertices are and

2 10 points Evaluate the integral a 5 points L b Spoints 4 x 1 dx

9 10 points Two cars start moving from the same point One travels south at 48 mi h and the other travels west at 20 mi h At what rate in mi h is the distance between the cars increasing two hours later

Use Stokes Theorem to calculate the circulation of the field F around the curve C in the indicated direction F 5yi 2xj 4z k C the portion of the plane 8x 5y 2z 10 in the first quadrant OA 3 15 B 4 O C 0 OD 15

9 Determine whether the series which is the sum from n 1 to infinity of the terms An 1 2n 1 converges or diverges

Find the value of the following function ata 4 and 5 Does the Intermediate Value Theorem guarantee that the function has a real zero between these two vales 700 31 21 7 Does the intermediate Value Theorem guarantee that there is a real zero between 4 and 57 Keypa Keyboard Shorts

Find the value of the following function at x 4 and x 5 Does the Intermediate Value Theorem guarantee that the function has a real zero between these two x values Answer f x x 3x 2x 7 f 5 Does the intermediate Value Theorem guarantee that there is a real zern between 4 and 5 Keypad Keyboard Shortcuts

Sonia s horticulture club is exhibiting at the city garden show Each garden must be bordered by 60 0 m of wood against a brick display wall What dimensions will maximize the area of the garden 10 m x 40 m 5 mx 50 m 15 mx 30 m 1 mx 58 m

A rectangle with sides parallel to the coordinate axes is inscribed in the region bounded by the graphs of y 36 x and y 2x 9 What is the maximum possible area of such a rectangle O 30 O 30 5 60 O 60 5

Determine if the ordered pair is a solution to the system of equations 10x 6y 12 6x 3y 27 a 3 3 55

Suppose that P dollars in principal is invested in an account earning 4 3 interest compounded continuously At the end of 4 yr the amount in the account has earned 1595 26 in interest Part 0 2 Part 1 of 2 a Find the original principal Round to the nearest dollar Hint Use the model A Pet and substitute P 1595 26 for A The original principal was approximately Part 1 2 Part 2 of 2 X b Using the original principal from part a and the model A Pe determine the time required for the investment to reach 15 000 Round to 1 decimal place Using the original principal from part a and the model A Pe it will take the investment approximately yr to reach X S

3 Two ships are sailing from Halifax The Nina is sailing due east and the Pinta is sailing 43 south of east After an hour the Nina has traveled 115km and the Pinta has traveled 98 km How far apart are the two ships to the nearest kilometer

10x 6y 12 6x 3y 27 a 3 3 b Part 0 2 Part 1 of 2 The ordered pair 3 3 Choose one Part 1 2 Part 2 of 2 a solution to the system of equations X 5