Calculus Questions

Find where x 2x 0 Write your answer in interval notation Round to one decimal place as needed Left Interval 8 Dight Interval Submit

Find where x4 2x 0 2 Write your answer in interval notation Round to one decimal place as needed Left Interval

X Find the real zeros of the given function Round to one decimal place as needed 4 x 2x Solution 1 Solution 2

Definite integrals from graphs Figure shows the graph of a tion f with the areas of the regions bounded by its graph and the x axis given Find the values of the following definite integrals x dx b 1 x dx a C f x f x dx d y A a f x dx 12 Figure y f x b 10 C d

3 and Properties of integrals Assume that fof x dx of x dx 10 Evaluate the following integrals if possible f2f x dx b f f x dx e So f x d c ff x dx d f6f x dx e

19 36 Sketch the region enclosed by the given curves and find its area 19 y 12x y x 6 20 y x y 4x x 21 x 2y x 4 y 22 y x 1 x y 1 23 y 2x y x 24 y x y x 25 y x y x 0 x 16 26 y cos x y 2 cos x 0 x 2 27 y cos x y sin 2 r

43 44 Evaluate the integral and interpret it as the area of a region Sketch the region 43 sin x cos 2x dx 44 13 2 dx

Homework Find the slope for each line 22 2x y 14 23 3x 2y 51 24 13 20x 5y

Consider a w N weight suspended by two wires as shown in the accompanying figure If the magnitude of vector F2 is 150 N find w and the magnitude of vector F N 42 F What is the weight w W N Type an integer or decimal rounded to three decimal places as needed W 31 F2

The table shows the numbers x of absences in a school year and the final exam scores y of several students Absences X Final Exam Score y Absences 1 7 0 5 0 94 69 98 77 97 6 1 4 2 6 Final Exam 73 93 81 89 72 Score y a Use a graphing calculator to find an equation of the line of best fit Round the slope and y intercept to the nearest integer b Interpret the slope and y intercept of the line of best fit c Approximate the final exam score of a student who has 3 absences a The line of best fit is b The slope is and the y intercept is So a student with 0 absences is expected to earn a points per absence decreases by about on the final exam and the score

11 18 Sketch the region enclosed by the given curves Decide whether to integrate with respect to x or y Draw a typical approximating rectangle and label its height and width Then find the area of the region 11 y x 2 y x 1 x 0 x 1 12 y 1 x y 2 x x 1 x 0 13 y 1 x y 1 x x 2 14 y cos x y e x 2 15 y x 2 y x 16 y x 4x y 2x 17 x 1 y x y 1

f 3500 is invested at an interest rate of 5 25 per year compounded continuously find the value of the investment after the given number of years Round your answers to the nearest cent a 2 years b 4 years c 6 years

When a certain medical drug is administered to a patient the number of milligrams remaining in the patient s bloodstream after t hours is modeled by D t 60e 0 5t How many milligrams of the drug remain in the patient s bloodstream after 2 hours Round your answer to one decimal place mg

An investment of 6000 is deposited into an account in which interest is compounded continuously Complete the table by filling in the amounts to which the investment grows at the indicated interest rates Round your answers to the nearest cent t 6 years Rate per year 1 2 3 4 5 6 Need Help Read It Amount

cosh x ex e x 2 a Sketch the graphs of the functions y e and y y 3 y cosh x 2 y BES 3 2 1 y 2 2 3 2 1 cosh x y 2 1 2 3 y 3 y cosh x 2 y 2 ex on the same axes and use graphical addition see Section 2 7 to sketch the graph of y cosh x y 3 y cosh x 2 b Use the definition to show that cosh x cosh x e x 1 2 3 X X 3 y 2 y 2 2 1 3 2 1 18 y 1 1 3 y cosh x 2 2 2 2 3 1 2 3 X X

Use a calculator to evaluate the function at the indicated values Round your answers to three decimals 5x g x 5 g 6 g 3 65

The function f x ex is called the natural Need Help Read It exponential function The number e is approximately equal to Round your answer to five decimal places

The function f x 3 is an exponential function with base Need Help Read It f 2 f 0 f 2 and f 6

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 6 pts Calculate the difference quotient of f x e and simplify it as was done in class 2 6 pts If 4 700 is invested at an interest rate of 4 5 per year compounded continuously find the value of the investment at the end of the given number of years Round your answers to the nearest cent a 2 years b 3 years c 6 years 3 8 pts What are the linear y ax b and exponential functions y a b whose graphs contain the points 0 5 and 3 320

a 4 pts What is the average rate of change of f between 3 and 2 Write the answer as a fraction no decimals or mixed numbers b 4 pts What is the equation of the secant line through 3 f 3 and 2 f 2 Use fractions in the equation no decimals or mixed numbers Sketch a graph of the function and this secant line 5 8 pts Sketch a graph of y 5e 7 What is its y intercept and what is the equation of its horizontal asymptote Fill in the blanks for the end behavior below too

pts Use tra lations to sketch the graph of domain off What is the range What is the equation of the asymptote 4 6 pts Rewrite each log equation as an exponential equation a log 3x 5 b log x 2 3 c In x 4 2 5 6 pts Rewrite each exponential equation as a log equation a 2 47 b 10x 450 80 now the asymptote What is the

a Set up an integral for the area of the shaded region b Evaluate the integral to find the area 1 ya 2 y 3x x y x 2 2 X YA y ex O 1 e 1 1 y x x

Solve the initial value problem dy da 1 8 T y S

0 B 22 Match each equation with a graph above 2 2 2 G R Question Help Video a red R b orange 0 c green G d blue B

Describe the long run behavior of f x 5 1 3 As a f x O As I f x Question Help Video Message instructor

Use a calculator to solve the following equation in the interval 0 2 correct to five decimal places 4 sin x 2 0 0 78540 2 35619 3 92699 5 49779 0 78540 0 78540 2 35619 3 92699 0 78540 2 35619 3 92699 5 49779 7 06858 0 78540 2 35619

Simplify the following trigonometric expression as much as possible 1 cos x sin x O sin x O cos x O 2 csc x O 2 sin x sin x 1 cos x

Solve the trigonometric equation in the interval 0 27 Give the exact value if possible otherwise round your answer to two decimal places Enter your answers as comma separated list 2 cos 0 17 cos 0 8 0 0

4 Find a formula for the exponential function passing through the points 2 and and 2 36 y Question Help Video Message instructor

Simplify the following trigonometric expression tan x cos x csc x 01 cot x O sin x sin x

TU Make the indicated trigonometric substitution in the given algebraic expression and simplify Assume 0 t 2 tan t O cos t 01 O sin t X 1 x X sin t

Use an addition or subtraction formula to find the exact value of the expression tan 255 0 1 3 O2 3 2 01 1 3 1 V 3

Simplify the following trigonometric expression as much as possible sec y tan y csc y csc y tan y sin y sec y

Find all solutions of the equation 2 sin x 1 0 Select the correct answer where k is any integer TU TU 6 TU 6 TU 6 2k KI 5TT 6 5TT Km KT 6 2k 2k 11 6 11 KT 2k

A cosmetic company gives sales training to its newly hired employees To determine how effective the training is the firm compared the monthly sales of a group that has completed the training with a group that has not The numbers to the right indicate thousands of dollars of sales last month Represent the two sets of data on a single stem and leaf display Does the orientation program seem to be succeeding Choose the correct answer below OA With Training No Training 51348 96212022234689 O C 99862337 8333247 With Training No Training 3481 5 02223468929621 37399862 7483332 With Training No Training 29 32 36 43 48 43 22 38 42 39 39 21 26 15 43 26 28 14 13 20 22 29 22 24 33 47 23 22 18 37 XX B With Training No Training 51348 9621 2022234689 99862337 7483332 D With Training No Training 833321348 96212022234689 99862337 74 5 Does the orientation program seem to be succeeding OA The orientation program is not working because employees who received training had lower sales values OB The orientation program is working because employees who received training had higher sales values OC The orientation program is working because employees who received training had lower sales values OD The orientation program is not working because employees who received training had higher sales values

On one ranch the farmer decided not to randomize the order of treatments and instead chose which cows received each treatment A researcher reminds the farmer that randomization helps minimize the influence of confounding variables in an experiment Which of the following could be a confounding variable in this setting Explain to the farmer how the cofounding variable could create a false perception of a relationship between markings and predator attacks if treatments are not randomized Gender of each Cow Age of each Cow Explain your thinking Size of the Number of Cows on the Farm

A twenty story hospital building with a 200 ft x 270 ft footprint is to be built on a site underlain by fill over glacial sands The building will have a 25 ft deep basement and will probably be supported on either a mat foundation located 5 ft below the bottom of the basement or a deep foundation extending about 100 ft below the bottom of the basement The groundwater table is about 30 ft below the ground surface and bedrock is about 165 ft below the ground surface There are no accessibility problems at this site a How many exploratory borings will be required as per NYC Code and to what depths should they be drilled b How would you obtain groundwater data Explain your answer

Find the horizontal asymptote of f x y 4x x 4 3x x 2

A car comes to a stop six seconds after the driver applies the brakes While the brakes are on the following velocities are recorded Time since breaks were applied seconds 0 1 5 3 4 5 Velocity feet per second 63 34 12 0 Give lower and upper estimates using all of the available data for the distance in feet the car traveled after the brakes were applied Lower Upper

28 fx x 2 dx

Suppose that a person is taking a walk along a long straight path and walks at a constant rate of 8 miles per hour a On the graph below sketch a labeled graph of the velocity function v t 8 9 mph 8 7 6 1 5 4 3 2 1 1 2 Clear All Draw hars 3 b How far did the person travel during the first hour the first two hours How is this distance related to the area of a certain region under the graph of y v t c Use part b to sketch the graph of the position function y s t assuming that s 0 0 9 imiler

Consider a W N weight suspended by two wires as shown in the accompanying figure If the magnitude of vector F2 is 140 N find w and the magnitude of vector F What is the weight w 48 F W 35 F2 W N Type an integer or decimal rounded to three decimal places as needed

s 6x 4x 6 dx Do not include the constant C in your answer For example if you found the antiderivative was 2x C you would enter 2x What is

In summarizing the results the researchers in the article state Ambush predators were less likely to kill cattle painted with artificial eyespots than unmarked and cross marked cattle The differences between the groups were statistically significant Would it be valid to claim that the painting of eyespots caused a reduction in attacks by predators Explain your choice Yes The claim is appropriate Explain your thinking No The claim is not appropriate

Find the following antiderivative 7x 3x 2 dx Do not include the constant C in your answer For example if you found the antiderivative was 2x C you would enter 2 x

An object moves with velocity as given in the graph below in ft sec How far did the object travel from t 0 to t 15 velocity f sec 9 8 7 6 5 4 3 2 1 5 10 15 20 25 30 time sec feet 35 40 45 a

9 54 Evaluate the indefinite integral 2 9 fx 1 x dx 11 ft e di 13 sin t 3 dt dx 4x 7 15 Sz 17 S cos e 1 sin 0 19 cos 0 sine de 21 eu de 4 2 du 10 5 3x dx 12 f sint 1 cost dt 14 f sec 20 de 16 y 4 y dy z 18 1 5r 20 fer dr 22 dz sin 1 x dx

your answer Note When entering natural log in your answer enter lowercase LN as In There is no natural log button on the Alta keyboard Sorry that s incorrect Try again

Suppose an object moves along a straight line The graph below shows the velocity of the object from t 0 seconds to t 10 seconds S 4 3 2 Velocity 1 2 3 5 Time 2 3 4 5 6 7 8 9 10 O Determine the intervals over which the object is moving forward moving backward or is stationary Report solutions using interval notation Over what interval s if any is the object moving forward Over what interval s if any is the object moving backward Over what interval s if any is the object stationary

The velocity of a particle moving along the x axis is given by f t 4 4t cm sec Use the graph of f t to find the exact change in position of the particle from time t 0 to t 4 seconds including units Change in Position