# Calculus Questions

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Calculus
Definite Integrals
For the region bounded by y 2x the x axis and x 2 determine which of the following is greater the volume of the solid generated when the region is revolved about the x axis or about the y axis 32T 3 When the region is revolved about the x axis the volume is Type an exact answer using as needed 16x When the region is revolved about the y axis the volume is 3 Type an exact answer using as needed
Calculus
Vector Calculus
Problem 1 Use the method of cylindrical shells to find the volume when the region bounded by y 1 x x 0 x 1 and the x axis and rotated around the y axis
Calculus
Application of derivatives
20 0 mL of water from a graduated cylinder is added to a beaker of water as shown below What is the new volume of water in the beaker 40 40 0 35 35 0 50 mL 40 mL 30 mL 20 mL 10 mL
Calculus
Application of derivatives
A chunk of sulfur has a volume of 5 95 cm What is the mass of this sulfur Density of sulfur 2 07 g cm 0 348 g O 2 87 g O 3 88 g
Calculus
Vector Calculus
Water has a density of 1 0 g mL Which of these objects will float in water Object I mass 50 0 g volume 53 1 mL Object II mass 71 7 g volume 51 4 mL Object III mass 100 0 g volume 50 0 mL OI only O I III II only O II III
Calculus
Application of derivatives
Perform the following conversion 6 69 m s 1h 60 minutes 60 seconds 1 minute 1km 1 609 mi 1km 1000m O 0 334 mi h 15 0 mi h O249 mi h 13 4 mi h mi h
Calculus
Application of derivatives
Find the following Simplify your answers completely f x 6x 9 g x 4 x a f g x 5x 5 b f g x 7x 13 c fg x d f g x 6x 33x 36 6x 9 4 x What is the domain of f g Enter your answer using interval notation x 4
Calculus
Application of derivatives
Determine the area enclosed by the functions g x 4x 3 and f x 6 x 2x 2 between x 4 and x 2
Calculus
Vector Calculus
Evaluate the indicated function for f x x2 1 and g x x 3 algebraically If possible use a graphing utility to verify yo answer f g t 5
Calculus
Limits & Continuity
Evaluate the function for f x x 3 and g x x 2 f g 1 f g 1
Calculus
Limits & Continuity
Find the following f x x 3 g x x 3 a f g x b f g x c fg x d f g x What is the domain of f g Enter your answer using interval notation
Calculus
Limits & Continuity
Consider the following graph 5 y 4 3 2 1 vertical shift of 3 units upward horizontal shift of 3 units to the left reflection in the x axis vertical stretch vertical shift of 3 units downward horizontal shift of 3 units to the right y Write an equation for the graphed function 5 4 3 Identify the parent function and describe the transformation shown in the graph Select all that apply 2 1 1 X
Calculus
Vector Calculus
Use a graphing utility to graph the three functions in the same viewing window f x x 3x 2 g x f x h x f 3x Describe the graph of g relative to the graph of f O g x is a reflection in the y axis O g x is a horizontal shrink O g x is a reflection in the x axis O g x is a horizontal stretch Describe the graph of h relative to the graph of f Oh x is a reflection in the x axis Oh x is a reflection in the y axis O h x is a horizontal stretch O h x is a horizontal shrink
Calculus
Limits & Continuity
g x x 3 8 a Identify the parent function f f x b Describe the sequence of transformations from f to g A horizontal shift 3 units to the left a reflection in the y axis and a vertical shift 8 units downward A horizontal shift 3 units to the right a reflection in the x axis and a vertical shift 8 units upward O A horizontal shift 3 units to the left a reflection in the x axis and a vertical shift 8 units upward O A horizontal shift 3 units to the right a reflection in the x axis and a vertical shift 8 units downward O A horizontal shift 3 units to the left a reflection in the x axis and a vertical shift 8 units downward c Sketch the graph of g by hand H O 10 10 5 5 y 10 5 5 10 y 10 5 10 5 10 10 X X d Use function notation to write g in terms of the parent function f Og x f x 3 8 O g x f x 3 8 O g x f x 3 8 Og x f x 3 8 10 10 5 5 y 10 5 5 10 y 10 5 5 10 5 5
Calculus
Application of derivatives
Compare the graph of the function with the graph of its parent function y X 1 Oy 8 is f x horizontally stretched 8 fold X X Oy y 8 is f x shifted to the left 8 units X Oy 8 X 8 Oy 8 X Oy 8 is f x is f x is f x shifted to the right 8 units 1 shifted down 8 units X vertically stretched 8 fold X
Calculus
Limits & Continuity
graph Determine which equation s may be represented by the graph shown Select all that apply Of x x 4 Of x 4 x Of x 4 Of x x 4 Of x x 4 Of x x 4
Calculus
Application of derivatives
Compare the graph of the function with the graph of its parent function y x The graph of y x is a vertical shrink of f x x The graph of y x is a reflection about the origin of the graph of f x x x is a reflection about either axis of the graph of f x x as f x f x x is a reflection in the x axis The graph of y The graph of y O The graph of y x is identical to the graph of f x x
Calculus
Limits & Continuity
Compare the graph of the function with the graph of its parent function y x 4 Oy x 41 Oy x 4 O y x 41 O y x 41 Oy x 4 is f x x shifted up 4 units is f x x vertically stretched 4 fold is f x x shifted to the left 4 units is f x x horizontally stretched 4 fold is f x x shifted to the right 4 units
Calculus
Limits & Continuity
Determine the convergence or divergence of the sequence with the given nth term If the sequence converges find its limit Limit equal O Converges Limit equal 3 2 Converges Diverges None of the above an In n 2n
Calculus
Application of derivatives
35 Velocity Use the results of Problem 33 to find the horizontal distance travelec by the bullet in 3 seconds Neglect the resistance of air on the bullet
Calculus
Vector Calculus
For each problem below the magnitude of the horizontal and vertical components of vector V are given In each case find the magnitude of V 27 Vx 30 V 40 29 Vx 35 0 V 26 0 31 Vx 4 5 V 3 8 28 V8 Vyl 6 30 Vx 45 0 V 15 0 32 Vx 2 2 V 5 8 33 Velocity A bullet is fired into the air with an initial velocity of 1 200 feet per second at an angle of 45 from the horizontal Find the magnitude of the horizontal and vertical components of the velocity vector 34 Velocity A bullet is fired into the air with an initial velocity of 1 800 feet per second at an angle of 60 from the horizontal Find the horizontal and vertical components of the velocity 35 Velocity Use the results of Problem 33 to find the horizontal distance traveled by the bullet in 3 seconds Neglect the resistance of air on the bullet 36 Velocity Use the results of Problem 34 to find the horizontal distance traveled by the bullet in 2 seconds 37 Velocity An arrow is shot into the air so that its horizontal velocity is 35 0 feet per second and its vertical velocity is 15 0 feet per second Find the velocity of the arrow
Calculus
Differential equations
Solve 2ydx x ln y In x 5 dy 0
Calculus
Application of derivatives
f x 6 3 2 using transformations Show the Vertical Asymptote and the y intercept 10pts Sketch
Calculus
Definite Integrals
Evaluate the following integral X 2 X 3 X x 3 dx dx
Calculus
Differentiation
Calculate the derivative of the following function y sin cos 5x dy dx 11 6 sin cos 2x cos 2x sin 2x
Calculus
Differentiation
Calculate the derivative of the following function y e4x 2x 9 6 dy
Calculus
Vector Calculus
For each problem below the magnitude of the horizontal and vertical components of vector V are given In each case find the magnitude of V 27 Vx 30 V 40 29 Vx 35 0 V 26 0 28 Vx 8 V 6 30 Vx 45 0 V 15 0
Calculus
Vector Calculus
Each problem below refers to a vector V with magnitude V that forms an angle with the positive x axis In each case give the magnitude of the horizontal and vertical components of V 19 V 40 0 30 21 V 13 8 0 24 2 23 V 420 0 36 10 20 V 40 0 60 22 V 17 6 0 67 2 24 V 380 0 16 40
Calculus
Application of derivatives
1 Analyze the following the polynomial f x x x 1 x 4 a Determine the degree of f x 2 points x x x 1 x u x4 x 1 x 4 x4 x x 4 X4x4x4 4 x x x 4 X5 4x4 x3 4x b What is the end behavior of f x 2 points 5 odd coet 1 Pos rise Answer c What are the zeros of f x and their multiplicities 2 points x x 1 x u 0 X 0 Multip 2 X multip 1 X UHP 1 x 4 Multip d What does each multiplicity of each zero found in c mean for the graph of f x 2 points x 41 0 x 4 0 Answer e What is the y intercept of f x 2 points Answer Answer 5 falls left fise fi x 0 12 x i ml X 1 MI X 4 MI
Calculus
Application of derivatives
Given the function f x x 6 a Find the inverse function f x f x State domains and ranges below using interval notation b1 Domain of original function f x b2 Range of original function f x c1 Domain of inverse function f 2 c2 Range of inverse function f x
Calculus
Definite Integrals
Construct a circle with radius r Then construct two hexagons H1 and H2 so that the circle is inscribed in H2 and encapsulating H1 H2 has apothem r and H1 has side r Set r 10 and calculate an upper and lower bound for the area of the circle by calculating the difference in the areas of H1 and H2
Calculus
Limits & Continuity
Let the function f be defined by the equation y f a where a and f x are rea numbers Find the domain of the function f x 49 4
Calculus
Indefinite Integration
b 0 75 m B Z 3 m 1 of 1 1 5 m y Determine the angle between cables AB and AC Suppose that a 1 8 m and b 1 2 m Eigure 1 Express your answer using three significant figures 0 Submit VASO It vec Request Answer Return to Assignment Provide Feedback www
Calculus
Application of derivatives
Calculus
Application of derivatives
tan 7 Round to seven decimal places as needed
Calculus
Application of derivatives
Simplify your answers Type exact answers using radicals as needed Use intege fractions for any numbers in the expression Rationalize any denominators csc 2190 2 sec 2190 cot 2190 3 Simplify your answers Type exact answers using radicals as needed Use intege fractions for any numbers in the expression Rationalize any denominators
Calculus
Application of derivatives
tan 0 1 0 pe an integer or a decimal Use a comma to separate answers as needed
Calculus
Application of derivatives
Calculus
Vector Calculus
Draw vectors representing the following velocities 1 30 miles per hour due north 2 30 miles per hour due south 3 30 miles per hour due east 4 30 miles per hour due west 5 50 centimeters per second N 30 W 6 50 centimeters per second N 30 E
Calculus
Indefinite Integration
5 Find the centerold of the region bounded by the graphs of Y X and X Y 6 X T 4
Calculus
Application of derivatives
Bearing A boat leaves the harbor entrance and travels 25 miles in the direction N 42 E The captain then turns the boat 90 and travels another 18 miles in the direction S 48 E At that time how far is the boat from the harbor entrance and what is the bearing of the boat from the harbor entrance See Figure 18 N 42 S 25 mi N 48 S FIGURE 18 18 mi
Calculus
Indefinite Integration
23 Bearing A boat travels on a course of bearing N 37 W for 79 5 miles How many miles north and how many miles west has the boat traveled
Calculus
Limits & Continuity
oblem 6 Which of the following series converge Problem 6 M8 IM8 1M8 C n 6 6n 6 7n 1 gn iii elln n 1 A i and iii only B iii only C ii and iii only D all of them E i and ii only F 1 or G none of them H ii only
Calculus
Application of derivatives
Problem 5 Determine which of the following series converge 77 1 5 2 n 4n n8 8n 6 n 1 n 3n n n A none of them B iii only C i and iii only D all of them E i only F i and G ii and iii only H ii only
Calculus
Definite Integrals
According to the integral estimate what is the smallest number of terms of the series n 1 be added in order to estimate its sum with an error that is less than 0001 that would have to
Calculus
Limits & Continuity
Foblem 5 Determine which of the following series converge 8T 5 2 4n n 1 n5 4n n8 8n 6 n 3n n n A none of them B iii only C i and iii only D all of them E i only F i and i G ii and iii only H ii only
Calculus
Differential equations
all values of 0 if 0 is in the interval 0 360 and has the given function value sin 00 5791576 C alue s of 0 is are an integer or decimal rounded to five decimal places as needed Use a comma to s
Calculus
Vector Calculus
17 If the distance between A and T on the map in Figure 19 is 0 5 inch find each of the following a The horizontal distance between Amy and Travis b The difference in elevation between Amy and Travis c The angle of elevation from Travis to Amy 0 1000 SO 1546 1 in 1600 ft Bishop Peak 1200 1600 Contour interval FIGURE 17 000 40 ft
Calculus
Limits & Continuity
0 1000 S 1546 1 in 1600 ft 1600 Bishop Peak 2002 Contour interval 40 ft FIGURE 17 18 If the distance between S and T on the map in Figure 17 is inch find each of the following a The horizontal distance between Stacey and Travis b The difference in elevation between Stacey and Travis c The angle of elevation from Travis to Stacey 19 Lompoc California is 18 miles due south of Nipomo Buellton California is due east of Lompoc and S 65 E from Nipomo How far is Lompoc from Buellton 20 A tree on one side of a river is due west of a rock on the other side of the
Calculus
Application of derivatives
Let f x be the number in thousands of computers sold when the price is x hundred dollars per computer Interpret the statements f 25 30 and f 25 6 Then estimate the number of computers sold if the price is set at 2525 pe computer What does f 25 30 imply OA When the price per computer is 2500 for every 100 price increase the sales increase by 30 000 computers OB When the price per computer is 3000 for every 100 price increase the sales increase by 25 000 computers OC 30 000 computers are sold when the price is set at 250 OD 30 000 computers are sold when the price is set at 2500