Calculus Questions

Consider the equation y 5 82e 0 0349t which is of the form y Aert to fill in the following blanks The r value for the equation is Therefore the type of change represented is because

For the following exercises consider this scenario For each year t the number of trees in Forest A is represented by the function A t by the function B t 94 1 025 1 Which forest s population is growing at a faster rate 2 Which forest had a greater number of trees initially 3 Initially by how many trees did the larger forest exceed the smaller forest 4 Which forest will have a greater number of trees after 30 years 5 After 30 years by how many trees will the larger forest exceed the smaller forest Round to two decimal places 100 1 015 In the nearby Forest B the number of trees is represented 4

Find the formula for an exponential equation that passes through the points 3 8 and 3 1 The exponential equation should be of the form y ab help equations Round a and b values to at least 5 decimals where appropriate

Let f x 3x 9x 12 4x 8x L 12 Domain Find the domain vertical asymptote s horizontal asymptote and select the correct graph help intervals Vertical Asymptote s Horizontal Asymptote If more than one enter values as a comma separated list help numbers help numbers

Let f x 9x 2 9x 9 Domain Find the domain vertical asymptote behavior of the function near the vertical asymptote and horizontal asymptote help intervals Vertical Asymptote a As x1 f x As a 1 f x Horizontal Asymptote y help numbers enter infinity or infinity help numbers enter infinity or infinity help numbers help numbers

Find an equation for a rational function f x that satisfies the following Vertical asymptote at x 8 and x 4 x intercepts at 3 0 and 6 0 y intercept at 0 36 f x help formulas

Find the formula for an exponential equation that passes through the points 0 5 and 1 1 The exponential equation should be of the form y ab help equations

For the function f x 6 5 find f 3 Round to five decimal places if necessary help numbers f 3

Let f x x 2x 8 x 6x 40 Identify the removable discontinuity Removable Discontinuity x help numbers

Minutes Cost 400 525 600 It takes you 4 seconds to climb up a 4 foot ladder that you are using to do a job You walt a seconds before climbing back down the ladder at the same rate Let x represent time and y represent height A Graph the function that models this problem B Write the piecewise function that represents the graph c Identify your domain and range 5 Height feet

You are walking from home to the grocery store which is 2 miles away Twenty minutes later and halfway to the store you realize that you forgot to bring money so you turn around return home and then walk back to the store Distance miles A Draw a graph that models your distance from home over time Assume that you are walking the same speed the entire trip B Your friend calls you 70 minutes after you began your trip and asks you how far away from home you are 2 0 La

Find the volume of the following solid The tetrahedron bounded by the coordinate planes x 0 y 0 2 0 and the plane 5x 3y z 15 0 The volume is cubic units Simplify your answer Type an integer or a fraction C

an You ride a bus that travels a total distance of 8 miles from the first bus stop to the last bus stop It takes the bus 4 minutes to travel 2 miles between each stop The bus walts 2 minutes at each stop There are 4 stops altogether Distance miles A Draw a graph that models the bus s distance over time beginning when the bus starts to wait a the first stop B How long does it take you to arrive at the last bus stop 10

Question 13 Given P x x 81 Write Pin factored form as a product of linear factors Be sure to write the full equation including P x

estlo 8 Divide and simplify 101 23i 7 3i

Simplify

Question 4 Perform the indicated operation simplify Express the answer as a complex number 62 5 Question Help Video 5314

Question 6 Perform the indicated operation simplify Express the answer as a complex number 8 10i 5 2i

Express 1 49 as a complex number 1 49

9 The graph of a piecewise function f shown in the xy plane for 8 x 8 Write the equation for f a 10 8 6 4 2 N 141 12 10 8 6 4 2 0 J 2 4 2 4 6 8 10 X

8 Let f x x 3 7 3x 15 x 2 x 2 x 2 Which of the following is true about f A f 2 1 B The graph of f x has an open circle at 2 3 C f 6 is undefined D f x has three distinct outputs at x 2

2 13x 25 x2 x The graph of f can be drawn with an open circle at 3 k Find the value of k x 3 3 x Let f x

5 Walgreens has the following pricing for 4x6 photo prints Quantity of 1 74 costs 0 37 each Quantity of 75 costs 0 25 each a Write a piecewise function C p that gives the cost of purchasing p prints b Patty ordered 70 prints then realized she was still short and ordered 10 more the next day Ho much did this mistake cost her Explain

2 The cost C in dollars of shipping a package that weighs w pounds can be modeled by the piecewise function given by 11 C w 0 w 2 2w 10 9 1 49w 6 1 99w w 10 a How much does it cost to ship a package that weighs 1 5 pounds b How much does it cost to ship a package that weighs 5 pounds c How much more does it cost to ship a package that weighs 10 pounds than a package that weighs

3 Graph the piecewise function given by 4 10 x 5 5 x 2 x 2 g x X 2 10 8 6 V 4 2 10 8 6 4 2 0 2 4 6 8 10 2 4 6 8 10

Use Newton s method with the specified initial approximation x to find x3 the third approximation to the root of the given equation Round your answer to four decimal place x5 x 7 0 X 1 x X3 3 2677

poster is to have an area of 210 in2 with 1 inch margins at the bottom and sides and a 2 inch margin at the top Find the exact dimensions that will give the largest printed area vidth 3 35 X in height 2 35 X in

Find the points on the ellipse 4x2 y2 4 that are farthest away from the point 1 0 1 4 2 3 3 x smaller y value x y x y 1 4 2 3 3 x larger y value

0 Describe the locus of points in a plane consisting of the centers of all circles with a radius of 2 cm that are tangent to the given line m Hint Do not assume that the locus has only one part

First Floor Second Floor Third Floor 13 15 14 16 11 9 22 38 40 39 The two way table shown above gives data on the connection preferences available from a local cable company in reference to the floor in which the apartment is located What is the marginal distribution of second floor connections Round to the nearest whole percent Internet Only Cable Only Internet Cable 11 6 39 36 42 117

9 20 Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function 9 g x t t dt 11 9 w sin 1 1 dt 13 F x 1 sect dt 10 g x f ln 1 1 dt t t 1 12 h u Hint 1 sec t dt f 1 sect dt dt

5 Waylon is back to school shopping with his mom at a large department store He s picked o the following items 3 pair of pants for 87 total 4 t shirts for 48 total 1 backpack for 35 1 hoodie for 26 1 pair of shoes for 37 When they get to the register they see this sign BIGGEST BACK TO SCHOOL SALE OF THE SEASON Spend 100 Spend 200 Spend 300 Spend 400 Save 10 Save 15 Save 20 Save 30 a How much will Waylon s purchases cost with the correct discount 1pt

Solve the inequality Enter your answer using interval notation x 7 x 3 x 1 0

Solve the inequality Enter your answer using interval notation 6x3x 9 54x

Name Instructions Use algebraic techniques to solve problems unless otherwise instructed Show the calculations leading to your answers except basic arithmetic Simplify and circle your final answers 1 A certain breed of mouse with an initial population of 30 was introduced onto a small island Scientists estimate that the mouse population doubles every year a 4 pts Find a function N that models the number of mice after t years b 4 pts Use the function to estimate the mouse population after 4 years and 6 years assuming that none have died

3 3 points Evaluate the following integral some need to be changed to other coordinates a b c 2y px y 6 1 1 y 0 IM LS 9 x 9 x y 1 x y ry dzdxdy 1 x y x y dzdydx x z y z z dzdxdy

e prime factorization is se ascending order

Solve the given equation Enter your answers as a comma separated list Let k be any integer Round terms to three decimal places where appropriate If there is no solution enter NO SOLUTION 2 sin 0 cos 0 1 8

Problem 5 a Find the value of c that satisfies the conclusion of the Mean Value Theorem for the function f x lnx on the interval 2 16 Problem 5 a Problem 5 b b If f 1 4 and f x 9 for 1 x 9 then according to the Mean Value Theorem what is the smallest possible value for f 9 c Let f be the function whose graph is shown below 3 N 3 y 2 1 0 0 1 2 4 X Estimate the two values of c that satisfy the conclusion of the Mean Value Theorem on the interval 2 7 5 6 7 8 Enter your answer symbolically as in these examples

An equation is given Enter your answers as a comma separated list Let k be any integer Round terms to three decimal places where appropriate If there is no solution enter NO SOLUTION 3 tan 30 1 0 a Find all solutions of the equation 0 b Find the solutions in the interval 0 2 8

An equation is given Enter your answers as a comma separated list Let k be any integer Round terms to three decimal places where appropriate If there is no solution enter NO SOLUT COS a Find all solutions of the equation 0 1 0 b Find the solutions in the interval 0 21 8

Solve the given equation Enter your answers as a comma separated list Let k be any integer Round terms to three decimal places where appropriate If there is no solution enter NO SOLUTION 2 sin 8 cos 8 1 8

Use a Double or Half Angle Formula to solve the equation in the interval 0 2 Enter your answers as a comma separated list sin 20 sin 0 0 0

Problem 8 Consider the following function f x est 5 8 5e x Problem 8 a Problem 8 b a Find the two horizontal asymptotes of f b Find the vertical asymptote of f Enter your answer symbolically as in these examples Enter your answer symbolically in th separate your answers do not include y in y

Problem 9 Suppose that the derivative of a function f is given by f x x x 2 6 x 3 5 x 4 Find the x coordinates of the local maximum points of f Problem 9 A 0 and 2 only G 2 and 3 only D B 3 and 4 only C 0 and 3 only D 2 and 4 only E 3 only F 0 and 4 only H 2 only

Problem 10 Suppose that the second derivative of a function f is given by f x x x 2 7 x 3 4 Find the x coordinates of the inflection points of f if any A 2 only B 2 and 3 only C 0 only D 0 and 2 only E 0 and 3 only F none G 3 o H 0 2 and 3

6 Let f x 1 e x On what interval is f increasing A In 6 B 0 In 6 C In 6 D In 5 0 E In 5 F In 5 0 G In 6 H ln 5

Problem 11 Evaluate the following limits 3 lim X 0 x5x 5x 1 b lim x5 tan 7 x5 X18 lim 1 X 8 7x

An artist wants to paint the interior of the shape shown below on the side of a building Meters y y 3 x Meters 9 X How much area in square meters will the artist need to paint Round your answer to two decimal place m

1 Maisy is an employee at a shoe store She receives a 20 discount on all items including sales items For Black Friday all boots at the store are discounted 40 Maisy grabs a pair of boots that are regularly sold for 80 and takes them to the register where her employee discount is applied to the sale price How much did Maisy have to pay for her boots