Calculus Questions

4 3 Points DETAILS SCALCET9 2 XP 8 003 Trace or copy the graph of the given function f Assume that the axes have equal scales Use estimates of the derivative off to skatch the graph of on the same coordinate axes 8 00 Do 20

Use the given graph to estimate the value of each derivative a f 3 b f 2 c f 1 d f 0 e f 1 f f 2 g f 3 y f x YA 1 0

6 3 Points DETAILS SCALCET9 2 XP 8 006 Trace or copy the graph of the given function f Assume that the axes have equal scales Use estimates y the derivative off to sketch the graph of f on the same coordinate axes

The graphs of four derivatives are given below Match the graph of each function in a d with the graph of its derivative in I IV YA ya a c ya YA 0 VA A X YA V II b d III YA M v IV

Use the reciprocal identities in the following problems 1 If sin 0 find csc 0 2 If cos 0 V3 2 find sec 0

x 1 2x 1 7 f x 2 1 x 4 1 2 2 x 3x a at x 1 x 4

8 g x 2x 1 In x a We x 3 3 x 1 x 1 x 3x 7 at x 3 raping ant sau b at x

4 r x 3x4 9x 2

3 f x X x 2x

A 4 ft tall fence runs parallel to the wall of a house at a distance of 7 ft Find the length of the shortest ladder that extends from the ground to the house without touching the fence Assume the vertical wa of the house is 20 ft high and the horizontal ground extends 20 ft from the fence The length of the shortest ladder is ft Round the final answer to the nearest tenth as needed Round all intermediate values to the nearest thousandth as needed

Let R be the region bounded by the following curves Let S be the solid generated when R is revolved about the given axis If possible find the volume of S by both the disk washer and shell methods Check that your results agree 1 9 y x y x in the first quadrant revolved about the x axis Set up the integral s that gives the volume of the solid as a single integral if possible using the disk washer method Use increasing limits of integration Select the correct choice below and fill in any answer boxes within your choice OA dx Type exact answers C B dx dx Type exact answers

6 For 60 90 determine if each statement is true or false V4 2 a b sin 0 0 cos 0 c tan 0 1 3 2 1 3

2 Evaluate a sin T b cos 0 c tan 5 d sin 45

If is an angle in the first quadrant and sin 0 0 2 V find tan 0 2

5 If is an angle in the first quadrant and cos 0 find in radians and degrees

4 Use the unit circle to estimate the values of sin 55 and cos 55 to the nearest tenth 0 5 55 O 0 5 0 05 0 5

3 Find the missing lengths of the sides of the triangle 2 45

1 Consider the angles 0 where 0 0 2 a What is the largest possible value of cos 0 At which angle measure 0 does it occur b What is the smallest possible value of cos 0 At which angle measure 0 does it occur c What is the largest possible value of sin 0 At which angle measure 0 does it occur d What is the smallest possible value of sin 0 At which angle measure 0 does it occur

Suppose f x 0 for all x and the y axis A Set up the integral that gives the volume of the solid Use increasing limits of integration Select the correct choice below and fill in the answer boxes to complete your choice Type exact answers 4 S 2x f x dx 0 OB S x dx The volume of the solid is Type an exact answer 0 f x dx 15 Let R be the region in the first quadrant bounded by the coordinates axes y f x and x 4 Find the volume of the solid generated by revolving R aroun CORA

Use the shell method to find the volume of the solid formed when a hole of radius 6 is drilled symmetrically along the axis of a right circular cone of radius 8 and height 12 Model the situation on a set of axes by placing the center of the base of the cone at the origin and the cone s axis along the positive y axis Set up the integral that gives the volume of the solid using the shell method Use nonnegative and increasing limits of integration Select the correct choice below and fill in the answer boxes to complete your choice Type exact answers OA S OB dy dx

Use a graphing utility to graph the function and to approximate any relative minimum or relative maximum values of the functio Round your answers to two decimal places If an answer does not exist enter DNE f x 5x 4x 9 relative minimum relative maximum x y x y

Let R be the region bounded by the following curves Use the shell method to find the volume of the solid generated when R is revolved about the y axis y 8 x y 0 x 1 and x 3 Set up the integral that gives the volume of the solid using the shell method Select the correct choice below and fill in the answer boxes to complete your choice Type exact answers OA B 1 3 1 dy 2x 8 x 0 dx The volume is Type an exact answer

onsider the following f x 2x a Use a graphing utility to graph the function y increasing 10 10 constant decreasing 5 5 10 5 5 10 y 10 5 5 10 5 5 10 10 X X 10 10 5 5 y 10 5 5 10 y 10 5 5 10 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 5

Consider the following x y 3 y 4 2 2 2 4 6 8 Use the Vertical Line Test to determine whether y is a function of x O Yes y is a function of x No y is not a function of x X Solve for y to describe how you can use a graphing utility to produce the given

Sketch the graph of the piecewise defined function x 7 3x 5 f x 20 20 x 4 X 4 y 20 10 1 0 20 y 20 10 20 10 10 20 20 X X 20 20 y 20 10 20 y 20 10 20 10 10 20 20

Let R be the region bounded by the following curves Use the shell method to find the volume of the solid generated when R is revolved about the x axis y x y 0 and x 25 Set up the integral that gives the volume of the solid Use increasing limits of integration Select the correct choice below and fill in the answer boxes to complete your choice Type an exact answer OA Sax dx OB dy y x

Identify the number of chiral centers present in Vitamin D3 shown below HO 4 2 3 Vitamin D3

Assume that the domain of f is the set A 2 1 0 1 2 Determine the set of ordered pairs representing the function f f x x 5 f 2 x y f 1 x y f 0 f 1 f 2 x y x y x y

Sketch the graph of a function with the given properties You do not need to find a formula for the function h 2 1 lim h x 4 lim h x 0 h 1 lim h x 3 lim h x 2 X 2 X 2 X 1 X 1 Which of the following is a graph that satisfies all of the given conditions A O C A Q 5 o S OB O D Q Q G Q

Evaluate the function at each specified value of the independent variable and simplify If an answer is undefined enter UNDEFINED f x a b 1 3x f 5 f 0 25 X 0 X 0 c f 5 II

One cubic centimeter of a typical cumulus cloud contains 380 water drops which have a typical radius of 10 pm a How many cubic meters of water are in a cylindrical cumplus cloud of height 3 0 km and radius 1 0 km b How many 1 liter pop bottles would that water fill c Water has a density of 1000 kg m How much mass does the water in the cloud have a Number i b Number i c Number Units Units Units

Antarctica is roughly semicircular with a radius of 2 00 x 103 km see the figure The average thickness of its ice cover is 3 00 x 10 m How many cubic centimeters of ice does Antarctica contain Ignore the curvature of Earth 8000 m 2000 km

The median player salary for the New York Yankees was 1 5 million in 2007 and 1 7 million in 2013 Write a linear equati giving the median salary y in terms of the year x Let y be in millions of dollars and let x 7 represent 2007 Use the equation to predict the median salary in 2027 Round your answer to one decimal place million

Determine the slope m and y intercept if possible of the linear equation If the slope is undefined enter UNDEFINED Enter NONE if there is no y intercept 5x 7y 1 slope m y intercept x y Describe its graph The line is vertical and passes through 2 0 O The line is horizontal and passes through 0 O The line passes through 0 1 and falls 7 units for each horizontal increase of 5 units The line passes through 0 1 and falls 5 units for each horizontal increase of 7 units O The line passes through 0 1 and falls units for each horizontal increase of units

m 6 5 8 12 Then use a graphing utility to plot the points and use the draw feature to graph the line segment connecting the two points Use a square setting 5 y 5 10 15 20 y 20 15 10 5 5 5 10 10 X 15 15 X O 15 15 10 10 5 5 y 20 15 10 5 y 5 10 15 20 5 X

Evaluate lim 7x 3x 5x X 0 X If an answer does not exist enter DNE 8 CO X

49 x x 7 x 7x If an answer does not exist enter DNE Evaluate lim

dentify the line that has each slope Li a m 0 0 41 042 OL3 b m 3 4 O 41 0 42 OL3 c m 1 0 41 042 L3 L

Determine the slope m and y intercept if possible of the linear equation If the slope is undefined enter UNDEFINED Enter NONE if there is no y intercept 2x 9y 1 slope m y intercept x y Describe its graph O The line passes through 0 1 and falls 3 3 units for each horizontal increase of units 9 The line passes through 0 1 and falls 2 units for each horizontal increase of 9 units O The line is vertical and passes through 2 0 O The line is horizontal and passes through 0 1

Limits Continuity Course Packet on computing limits from graphs The graph of y f x is shown below 1 y 2 1 2 2 3 Use the graph of y f x to compute each of the following values If an answer does not exist e f 1 DNET Enter a number lim f x DNE

3 For each function find the inverse the domain and range of the function domain and range of the inverse and determine whether the inverse is a functi a f x x 7 b f x 2x 2 c f x x d g x 2x 1 3

below A B C owing questions about the function f whose graph is show graph of the function f Find lim f x 2 Find lim Find lim h 0 0 h f 0 1 does h 2 h Find lim f x undhud x 0

Question Find the total area between the curve of the function f x x 1 and the x axis over the interval 9 5

Ose the graph of f x log 4x to graph the function f x log 4 x 1 3 Use the graphing tool to graph the function Click to enlarge graph Ay

Question pod area between f x and the x axis over the interval

Question What is the net signed area between f x 2x 2 and the x axis over the interval 8 5 Do not include any units in your answer Provide your answer below IE

Find the net signed area between the curve of the function f x 2x 4 and the x axis over the interval

Find the volume of the solid generated when the region bounded by y x and y 2 x is revolved about the x axis Set up the integral that gives the volume of the solid 10 dx 0 CHILD

Find the net signed area between the curve of the function f x 2x 4 and the x axis over the interval 7 3 Do not include any units in your answer

Find the volume of the solid generated when R shaded region is revolved about the given line y 1 x y 1 x 1 about y 1