Calculus Questions

List all the x intercepts Select the correct choice below and if necessary fill in the answer box es to complete your choice OA The graph has two x intercepts The leftmost x intercept is rightmost x intercept is Type integers or decimals OB The graph has one x intercept Type an integer or a decimal OC There are no x intercepts and the 0 8 1 Ay

Question Provide your answer below SAT Y 5 4 3 2 1 3 6 g x 9 f x 4x x g x 4 x 8 h x 216 30x x 12 h x 15 18 x Use the formulas for areas of triangles and circles to evaluate the integrals of the functions graphed in the figure Enter the sum of all shaded areas in terms of

1 point Evaluate the Riemann sum for f x 6x 4x with n 6 taking the sample points to be right endpoints Illustrate with a diagram Riemann sum is 0 x 3

Find the x intercept s and y intercept of the graph of the equation y 10x 6x 5 What are the x and y intercepts OA There are zero x intercepts and a y intercept at OB There is one x intercept at and a y intercept at OC There are two x intercepts at and and a y intercept at

Without sketching the graph find the x intercepts and y intercepts of the graph of the equation 7x 3y 21 Select the correct choice below and if necessary fill in the answer box to complete yo choice OA The x intercept s is are Type an integer or a simplified fraction Use a comma to separate answers as needed OB There are no x intercepts

6 Evaluate Ix 41 dx using a geometric formula Provid

1 point Use the midpoint rule with n 4 to approximate the integral 6 C x dx

1 point The table below gives the values of a function obtained from an experiment x f x Using three equal subintervals with left endpoints 2 f x dx Using three equal subintervals with midpoints 2 f x dx 6 3 1 7 2 1 Use the values in the table to estimate x dx in three different ways Using three equal subintervals with right endpoints f x dx 8 0 7 9 0 5 10 1 5 11 12 3 2 3 9 Suppose that f x is known to be an increasing function Will your estimate using right endpoints be an overestimate or an underestimate for the exact value of the integral Will your estimate using left endpoints be an overestimate or an underestimate for the exact value of the integral Will your estimate using midpoints be an overestimate or an underestimate for the exact value of the integral underestimate

1 point If f x dx 16 6 and f f x dx 4 8 find f x dx f x dx m B

Previous Problem 1 point Given that 0 Problem List Next Problem 16 27x 36 dx 2628 292 1944 calculate S 27 u 36 du 16 27u u 36 du

1 point Evaluate the integral by interpreting it in terms of areas 2 4x dx

1 point Evaluate the integral by interpreting it in terms of areas 8 6 8 64 x dx

Find the intersection of the line x y z 1 4 2 t 1 1 3 and the plane 2z4y 7z 26 0 An airplane is flying at an air speed of 420 km h on a heading of 210 A 45 km h wind is blowing at a bearing of 230 Determine the bearing and ground velocity of the airplane using geometric vectors

49 x 2 2 dx If applicable enter your a r Use the formula for the area of a circle to calculate answer in terms of it

Problems 15 and 16 refer to Figure 18 D FIGURE 18 15 Find AB if BC 4 BD 5 and AD 2 A B C

Problems 9 through 14 refer to Figure 17 Remember The sum of the three angles in any triangle is always 180 C A D FIGURE 17 B 9 Find a if A 30 10 Find B if 45 11 Find a if A a 12 Find a if A 2a 13 Find A if B 30 and a 100 14 Find B if a B 80 and A 80

Find a function f and a positive number a such that f x a f f t dt 2 2 dt 6x

10 Provide your answer below ag 54 Co 2 H 32 6 69 f 2 62 1 g z 1 12 71 h z 4 12 12 h z 12 15 Evaluate the integrals of the functions graphed using the formulas for areas of triangles and circles Enter the sum of all shaded areas in terms of t

y 2 arcsin 1 x ln 1 x 1 X y

cos uv u e x y V X 12

z x Examine z dy for extremum the function 3 r 6ru

Find and sketch an angle that is complementary to the angle O 11 79 179 101 79

There are 320 available to fence in a rectangular garden One side of this garden will be next to a road The fencing for the side of the garden next the road costs 6 per foot and the fencing for the other three sides costs 2 per foot Find the dimensions of the largest possible garden Dimensions x includo hoin funite in

curve is given by y L x where 0 x 1 represents the lowest fraction of the population of a society in terms of wealth and 0 sys1 represents the fraction of the total wealth that is owned by that fraction of the society Use this information to complete parts a through g Click the icon to view an example of a Lorenz curve 0 2A 1 Therefore G 2A 1 2 L x dx by the 0 Simplify transitive property completing the proof e Compute the Gini index for the cases L x xP and p 1 3 1 9 2 3 4 The Gini index for p 1 3 is 0 130 Type an integer or decimal rounded to three decimal places as needed The Gini index for p 1 9 is 0 310 Type an integer or decimal rounded to three decimal places as needed The Gini index for p 2 is 0 333 Type an integer or decimal rounded to three decimal places as needed The Gini index for p 3 is 0 500 Type an integer or decimal rounded to three decimal places as needed The Gini index for p 4 is 0 600 Type an integer or decimal rounded to three decimal places as needed f What is the smallest interval a b on which values of the Gini index lie for L x xP with p 1 Points 0 52 of 1 points Save

A rectangular garden of area 75 square feet is to be surrounded on three sides by a brick wall costing 10 per foot and on one side by a fence costing 5 per foot Find the dimensions of the garden that minimize the cost of materials Dimensions x include help units in your answers

Find the maximum value of Q xy provided x y 18 Maximum Value Also list the x and y values where this maximum occurs 1 x 0 0 2 y

cal numbers of th following Answer Formats If the function does not have any enter NONE f x x 6x 19 x

Consider the following function f x on the interval 6 3 f x x 16x 62 Absolute Maximum 1 Find the value where the Absolute Maximum occurs on the given interval 2 Find the Absolute Maximum Value of f x on the given interval x Maximum Value Absolute Minimum 1 Find the value where the Absolute Minimum occurs on the given interval 2 Find the Absolute Minimum Value of f x on the given interval x Minimum Value

Answer Formats f x 2x 15x 84x 12 x If the function does not have any enter NONE If the function has more than one type your answer as a comma separated list For example m

Find all critical numbers of the following function Answer Formats If the function does not have any enter NONE f x 3 4x 6x x

A farmer has 1500 available to build an E shaped fence along a straight river so as to create two identical pastures The materials for the side parallel to the river cost 6 per foot and the materials for the three sections perpendicular to the river cost 5 per foot Find the dimensions for which the total area is as large as possible Dimensions x include help units in your answers

Find all critical numbers of the following function Answer Formats If the function does not have any enter NONE f x x 14x 54 0 x

Find the positive numbers and y that minimize S x y provided xy 36 x Minimum Value The positive and y values where this minimum occurs 1 x 2 y 0

graph of a function y f x is given below Evaluate the following integrals by interpreting them in terms of areas 3 12 1 12 co 3 y f x 5 10 6 7 4 f 2 dz O S4 4 f x dx 10 S 4 4 f x dx 8 9 10

Oil leaked from a tank at a rate of r t liters per hour The rate decreased as time passed and values of the rate at two hour time intervals are shown in the table In this problem we are going to estimate the total amount of oil that leaked out during this ten hour time period t hours 0 2 4 6 8 10 r t L hr 9 4 7 7 7 3 5 9 4 8 4 1 Rate of Oil Leakage Left Endpoint Approximation Estimate the total amount of oil that leaked out using left endpoints Total Amount of Oil Right Endpoint Approximation Estimate the total amount of oil that leaked out using right endpoints Total Amount of Oil liters liters

The speed of a runner increased steadily during the first three seconds of a race Her speed at half second intervals is given in the table In this problem we are going to estimate the distance that she traveled during these three seconds 3 t seconds 0 0 5 1 1 5 2 2 5 v ft s 0 6 3 11 3 14 6 18 2 19 4 20 1 Speed of the Runner Left Endpoint Approximation Estimate the distance traveled by the runner using left endpoints Distance Right Endpoint Approximation Estimate the distance traveled by the runner using right endpoints Distance feet feet 4

Complete the table f s S f s Is 21 S 2 0 1 3 2 N G 4

nd all values of x such that f x 0 Enter your answers as a comma separated f x 4x 7

Evaluate the function at each specified value of the independent variable and simplify If an answer is undefined enter UNDEFINED f x 9 a b 9 2x c 8x 1 f 4 f 0 f 1 x 0 0 x 1 x 1

Assume that the domain of f is the set A 2 1 0 1 23 Determine the set of ordered pairs representing the function f f x x 7 f 2 x y f 1 f 0 f 1 f 2 x y C x y x y x y

valuate the function at each specified value of the independent variable and simplify If an answer is undefined enter NDEFINED q t a b c 6t 7 9 2 q 0 q x

valuate the function at each specified value of the independent variable and simplify If an answer is undefined enter NDEFINED g y 5 3y a g 0 b g c g s 3

valuate the function at each specified value of the independent variable and simplify If an answer is undefined enter NDEFINED g y 5 3y a g 0 b g c g s 3

Consider the following f x 7x 3 x a Use a graphing utility to graph the function 10 increasing 10 5 decreasing 5 20 10 10 20 10 10 20 5 5 10 10 X X 10 10 5 5 20 10 20F 20 10 0 20 5 b Determine the open intervals on which the function is increasing decreasing or constant Enter your answers using interval notation If an answer does not exist enter DNE 5

ketch the graph of the piecewise defined function 3 x x 1 h x y 10 10 5 5 J J 5 5 10 5 5 10 10 10 if x 0 if x 0 10 5 y 10 5 5 5 X 10 10 X 10 y 10 5 5 5 5

Use a graphing utility to graph the function and estimate its domain and range Then find the domain and range algebraically Enter your answers using interval notation X 41 domain range f x

Use the graph of the function to find the domain and range of f Enter your answer using interval notation domain range b f 1 c d LLLLLLL f 3 y 16 15 f 1 652229LSSOHNWA51 14 13 12 11 5 4 3 2 1 1 10 8 Use the graph to find the indicated function values a f 2 2 3 4 5 y f x 1 2 3 4 HA 5 6 X

The following limit is a definition of f a Determine the function f x and the value of a 4 h 4 h TH lim h 0

The limit below is a definition of f a Determine the function f x and the value of a lim h 0 f x 2 5 h 0 4 h

Compute the following limit 9x 7 9x 2 lim 818 Select the correct choice below and fill in any answer boxes in your ch A lim X 8 9x 7 9x 2 Type an integer or a simplified fraction B The limit does not exist