Calculus Questions

The absolute maximum value of f x x 12x on the closed interval 1 4 occurs at x OA 2 OB 0 OC 2 OD 4 E Cannot be determined

47 Use your calculator to estimate f sin x 2 dx OA 3 628 OB 40 078 OC 4 734 OD 7 875 OE 4 320

Use your calculator to estimate 4 sin 22 dx 4 OA 3 628 OB 40 078 O C 4 734 OD 7 875 OE 4 320

Use your calculator to estimate to three decimal places 3 2 cos x dx OA 0 282 B 6 919 C 3 736 D 3 459 E 0 564

The population of ground squirrels in a public park is measured to be 100 The growth of the population over time can be modeled by P t 600 1 5e 0 5t with P representing the number of squirrels and t given in months after the initial population measurement According to this model what is the maximum number of squirrels the park can support

Use your calculator to estimate OA 3 315 B 4 021 O C 0 417 OD 0 221 OE 0 767 1 dx

O A 1 000 OB 0 693 OC 2 000 OD 0 632 OE 2 914

O A 1 000 OB 0 693 O C 2 000 OD 0 632 O E 2 914 LO J ax

Given that f x is continuous f x dx 7 f f x dx 3 and 4 S f x dx 2 Then f f x dx A 2 B 6 C 3 D 4 E O

Suppose that f x is continuous and that 5 x dx 3 x dx 2 and 3 x dx 1 Then 3 3 3 f x dx OA 5 OB 6 OC 3 OD 6 OE 3

Given that fx dx 63 0 and 3 xdx A 121 5 OB 49 5 OC 256 5 OD 274 5 13 5 then f 3x 5x dx E Can t tell from the information given

1 Use the graph to estimate the intervals on which the 2 x function is increasing f x x 3 2 For each function graphed estimate the intervals on which the function is increasing and decreasing 4 4 4 B 6 my mi 5 EN P 220 SEN

graph y f x 10T 81 41 21 2 3 III 4 Consider the following statements 1 f x dx f x da I below 5 II 1 f z dz f z dz dx dx 5 OA I only B II only C III only D II and III only c5 3 f ar da f x d dx Which of the above statements is true 6

Systolic blood pressure levels above 120 mm Hg are considered to be high For the 100 systolic blood pressure levels listed in the accompanying data set the mean is 123 62000 mm Hg and standard deviation is 14 30602 mm Hg Assume that a simple random sample has been selected Use a 0 05 significance level to test the claim that the sample is from a population with a me greater than 120 mm Hg Click the icon to view the data set of systolic blood pressure levels Identify the null and alternative hypotheses Ho H V Type integers or decimals Do not round Systolic Blood Pressure Levels 100 106 116 116 130 158 114 122 132 126 128 134 104 126 130 114 132 136 112 126 134 130 136 158 106 x

Find limx 6 x 12x 36 x 6 O A Does not exist OB 36 O C 0 OD CO O E co 8

Find lim 6 x 12x 36 x 6 O A Doe s not exist OB 36 O C O O D D 00 OE 8

The graph of y x 4 5x5 10x4 5x 10 is concave upward for all values of x such that A 0 x 4 B x 4 or x 1 C 4 x 1 D x 0 or x 4 E all real x

M Which of the following represents the graph of f lx OA None of these OB n M O C O D

Luvusta 5 v hennet n muuttuja x Muuttuja x kerrotaan luvulla 13 ja tulo lis t n luku 9

M Which of the following represents the graph of f lx like uns OA None of these OB C OD V A

If the graph of f x looks like M Which of the following represents the graph of f lxl A None of these B C m VV

Find the indicated root of the given equation to at least four decimal places by using Newton s method Compare with the value of the root found using a graphing calcu 5x4 6x 5x 2x 3 0 between 1 and 0 The solution obtained by using Newton s method is approximately Round the final answer to four decimal places as needed Round all intermediate values to seven decimal places as needed

or a certain electric circuit the current in A is given by i 4 31e 52 4t di sin 219t where t is the time in s Find the expression for dt HILF E

A metai bar is heated and then allowed to cool Its temperature T in C is found to be T 5 25e 0 30t where t in min is the time of cooling Find the time rate of change temperature after 10 0 min After 10 0 minutes the time rate of change is degrees per minute Round to three decimal places as needed

The x and y coordinates of a moving particle are given by the parametric equations below Find the magnitude and direction of the velocity for the specific value of t Sketch the curve and show the velocity and its components x 3t y 1 t t 4 Find the magnitude of the velocity of the particle for the specific value of t The magnitude is approximately Type an integer or decimal rounded to two decimal places as needed

The vertical displacement y in cm of the end of an industrial robot arm for each cycle is y 3 2 Its vertical velocity for t 18s is cm s Round to the nearest tenth as needed tan 0 5t where t is the time in s Find its vertical velocity for t

Find the values of x for which the given function is concave up the values of x for which it is concave down and any points of inflection 3 y x 8x 8x 13 When is the graph of y concave up A 0 x 4 B x 0 C x 4 D x 0 and x 4

When a circular plate of metal is heated in an oven its radius increases at a rate of 0 03 cm min At what rate is the plate s area increasing when the radius is 41 c cm min The rate of change of the area is Type an exact answer in terms of

Find any local maximum or minimum points of the given function y x 4x 3x 1 Select the correct choice below and if necessary fill in the answer box to complete your choice OA The local maximum point s is are Simplify your answer Type an ordered pair using integers or fractions Use a comma to separate answers as r

Heat flows normal to isotherms curves along which the temperature is constant Find the line along which heat flows through the point 4 5 when the isotherm is along graph of 2x y 57 The equation of the line along which heat flows is y

10 8 6 Choose the correct statement lim f x 18 X 1 2 lim f x x 1 8 6 4 2 0 2 4 6 8 1 2 4 CO 6 8 I 1 19 10

10 8 6 lim f x x 2 4 Choose the correct statement x x 0 2 104 8 9 6 4 2 02 6 8 10 fx 2 4 6 8 10

P7 10 8 6 lim f x 00 X 4 4 Choose the correct statement lim f x 2 8 4 6 8 10 2 4 6 8 10 X

Let F x 2 tan x 3 where x 1 1 2 Find the inverse function F 1 x show work of f and the Domain and Find the range range of

5 4 155 Find the following limits a lim f x b lim f x H112 112 7 Y 3 2 1 0 b 1 2 3 4 c lim f x x112 1 d lim f x 1 3 4 e lim f x H15

v 20 3 Find the following limits a lim f x O U 3 2 0 2 1 P 1 2 b lim f x c lim f x 88 4 1 2 d lim f x e lim f x 1 lim f x X 5

F 10 8 6 lim f x 00 X 3 lim f x x 3 4 Choose the correct statement 2 lim f x is neither norm 8 6 8 4 0 2 10 2 4 6 2 I 1 4 6 8 10 O X

Which points on the curve of x xy y2 5 have vertical tangent lines O A 1 2 O B 2 1 and 2 1 O C 0 5 O D 4 2 and 4 2 OE There are no vertical tangents to this curve

Find da 9 x for g x sin x 5x OA sin x 20x OB sin x OC cos x OD sin x 120 OE cos x 120 x

A particle moves along the x axis so that its velocity at any time v t 2n 5 t sin nt A Find the acceleration at any time t 6 points is given by B Find the minimum acceleration of the particle over the interval 0 3 12 points

3 Consider the function h x a 2x 1 5 b where a 0 and b 0 are constants A Find h x and h x 6 points B Show that his monotonic that is that either halways increases or remains constant or h always decreases or remains constant 12 points

4 Consider g x x x 2 if x 2n 5 A Find the values of a and b such that g x is a differentiable function 12 points to B Write the equation of the tangent line to g x at x 2 9 points

1 The radius r of a sphere is increasing at a constant rate of 0 05 meters per second A At the time when the radius of the sphere is 12 meters what is the rate of increase in its volume 12 points B At the time when the volume of the sphere is 36 cubic meters what is the rate of increase in its surface area 15 points

The altitude of a kite is graphed here the y axis is in increments of ten feet the t axis is in minutes Over which intervals is the kite accelerating upward C N V O A Cannot be determined OB 3 6 3 OC 0 1 5 U 4 5 7 75 OD 0 3 U 6 3 10 OE 0 10

Find limx 3 5 2 Remember that x is the greatest integer function x O A 3 5 1 OB 3 5 OC 0 OD 2 3 5 O E Does not exist

Find lima 3 5 2 Remember that x is the greatest integer function x OA 1 OB 3 5 O C 0 O D 1 3 5 2 3 5 OE Does not exist

Which of the following could be the units for if y is the surface area of a tumor and x is the radius of the tumor O A Millimeters per centimeter OB Meters per radian O C Meters per second OD Gallons per hour E Square millimeters per millimeter

Does the graph represent a function that has an inverse function Q 10 10

es the graph represent a function that has an verse function 10 10 10 10 Q Q

10 8 6 Choose the correct statement lim f x 00 x 1 x x 2 8 8 6 4 0 2 6 8 10 4 1 10