Calculus Questions

Find the period y tan 5x Graph the function 10 15 Sn H 4 n 5 5 S 10 10 5 2 Sx 2 1 5 15 3 3 S 10 X 24 2x 3x 10 14 HA A 10 5 101 10 S 10 A 10 32 ff

Find the period y cot x Graph the function

Find the period Y 3 tan 3x Graph the function M HUSAIN

In Problems 1 3 find the general solution draw a phase portrait and determine whether the equilibrium point at the origin is asymptotically stable stable but not asymptotically stable or unstable 1 dx dt 2 51 4 2 X

Problem 6 Problem 6 Let F x f xf x Suppose that 4 5 4 2 and f 10 5 Find F 2 185

Find the period y tan x Graph the function AS AW A

3 3 points For each function below find the limit as x y approaches 0 0 or show i does not exist a f x y b f x y c f x y Hint try a path of the form y xP for a particular p x6 y x y 2y 9x 9y 2 x 3y sin y y

For the data given below answer parts a through f 5 6 9 11 13 X y Ay 20 O 2 3 a Draw a scatter plot Choose the correct graph below O A 3 5 4 6 20 2 B 7 8 15 20 Q G OC 20 O D 20

Graph the function f x 6 sin x y 5 5 0 7 y

As a wave passes by an offshore piling the height of the water is modeled by the function h t 8 cos t where h t is the height in feet above mean sea level at time t seconds trough crest a Find the period of the wave S b Find the wave height that is the vertical distance between the trough and the crest of the wave ft

Find the amplitude period and horizontal shift of the function y 8 sin 8 sin 3 x amplitude period horizontal shift Graph one complete period y TAJA 5 3 Z 3 O Nood Heln 2 84 9 y 8 6 Which y 8 6 y 6 2 3 I

plituc and period of the function and sketch its graph y 4 sin 2x amplitude period Sketch the graph of the function y y MA AN O 2 Need Help Read It Watch Master II 2 X y 3x 2 X

Find the amplitude and period of the function y 4 sin x amplitude period Sketch the graph of the function y 12 9 6 3 10 5 AAMA son 12 9 6 3 6x 9 12 3 5 10 10 y 10 9 12x 5 AA 12 97 6x 3x 3x 9x 12 157 10 x 10 12 9 6 3x y 10 5 10 3A 9x

Graph the function h x 3 cos x y 0 0 34 X m nu 2A

Graph the function f x 6 S sin x SH O 7L

Graph the function f x 5 sin x O GL y 41 O 41 2

9 Using first principles determine the equation of the tangent line at point 1 13 on the curve f x x 5x 7 5 mark

Find the slope of the tangent line at point 1 2 on the curve f x 5x 2x using First Principles 4 marks

The acceleration function in m s2 and the initial velocity v 0 in m s are given for a particle moving along a line a t 2t 2 v 0 15 Ost 5 a Find the velocity in m s at time t m s b Find the distance traveled in m during the given time interval m

Theorem If f is integrable on a b then f x dx heorem f x dx lim f x 4x 118 where Ax and x a iAx Use the given theorem to evaluate the definite integral b a n x2 4x 7 dx

Graph the given system of inequalities Choose the correct answer below O A 6 O C 6 x 2y 2 x 2y 2 6 x 2y 2 6 x 2y 2 OB x 2y 2 6 O D 6 6 x 2y 2 No Solution 6 4 2 6 4 2 2 4 6 2 N 4 A

Evaluate the indefinite integral Use C for the constant of integration sin t 1 cos t dt 3 2 cos 1 1 cos 1 3 sin 1 C

Graph the system of linear inequalities Tell whether the graph is bounded or unbounded and label the corner points x 0 y 20 4x y 20 x 4y 20 Use the graphing tool to graph all four inequalities in the system Then use the paint can icon to fill in the region that solves all of the inequalities Click to enlarge graph 22 20 18 16 44 12 10 8 6

Use a graphing utility to graph the function and the damping factor of the function in the same viewing window f x 5x sin x X Analyze the graph of the function using the method in Example 6 Enter your answers as a comma separated list Use n to represent an arbitrary integer if necessar y te touches y e sin x at y ex sin x has x intercepts at 2 X X

Use a graphing utility to graph the function include two full periods Graph the corresponding reciprocal function in the same viewing window y csc 4x KIN 1 Need Help ULUI U Read It 2 2 1 KIN KIN X IN Tat 4 2 y 2

Use a graphing utility to graph the function Use the graph to determine the behavior of the function as x c f x sec x a x f x b x f x f x TL f x 2 T 2 as x approaches from the right right 2 2 TU d x as x approaches from the left 2 TU as as x approaches from the right 2 as x approaches from the left

Match the function with its graph g x x cos x 2 0 2 4 6 2 2 2 my m 2 4 O 6 4 2 4 5 2 5 4 MM 2T 0 2 02 27 Describe the behavior of the function as x approaches zero As x 0 f x 2 4 5 5 02 0 2 2T 2T

Use a graph to solve the equation on the interval 2x 2r List the solutions in increasing order from left to right on the x axis csc x 2 3 3 x X X X smallest value largest value

Use the graph of the function to answer each question 2x sxs 20 f x cot x a Find all x intercepts of the graph of y fx Enter your answers as a comma separated list If an answer does not exist enter DNE b Find all y intercepts of the graph of y fx Enter your answers as a comma separated list If an answer does not exist enter DNE yu decreasing c Find the intervals on which the graph of y fx is increasing and the intervals on which the graph of y f x is decreasing Enter your answers using interval notation If an answer does not exis increasing d Find all relative extrema if any of the graph of yfx Enter your answers as a comma separated list of ordered pairs If an answer does not exist enter ONE relative minima relative maxima MY NOTES e Find all vertical asymptotes if any of the graph of y f Enter your answers as a comma separated list If an answer does not exist enter DNE A

Question 5 10 points The length L in cm of a pendulum is slowly decreasing at the rate of 0 100 cm s What is the time rate of change of the period 7 in s of the pendulum when L 16 0 cm if the equation relating the period and length is T L 245 T Paragraph E BI U A V OB 0 v I

Find the equations of the tangent and normal lines to the parabola with vertex at 0 3 and focus at 0 0 where x 1 Graph the curve and lines Paragraph V B I UA 00 GO v I X

Use the graph of the function to determine whether the function is even odd or neither f x sec x 2 The function is even O The function is odd O The function is neither even nor odd

Question 7 10 points A metal sphere is placed in seawater to study the corrosive effect of seawater If the surface area decreases at 35 cm year due to corrosion how fast is the radius changing when it is 12 cm Paragraph V B I U A Stm 0 v X

An engine cylinder 15 0 cm deep is being bored such that the radius increases by 0 100 mm min How fast is the volume V of the cylinder changing when the diameter is 9 50 cm Paragraph V BIU A v v I On v

Question 3 10 points Find the second derivative of the given function for the given value of x W a y 3x 3 2 b 11 X y 3 1 2x Paragraph v BIU A E E 00 0 v

Find dy dx in the following implicit function x x y x y Paragraph V BIU A v 11 00 Ins

Follow the steps for graphing a rational function complete your choice A R x B R x cannot be factored further graph the function R x OA R x Type your answer in factored form Do not simplify X 6 x x 13 What is the domain of R x 13 U 13 0 U 0 00 Simplify your answer Type your answer in interval notation Use integers or fractions for any numbers in the expression Write R x in lowest terms Select the correct choice and if necessary fill in the answer box to complete your choice Simplify your answer B R x is already in lowest terms Locate the intercept s of the graph Select the correct choice and if necessary fill in the answer box es to complete your choice OA The graph has x intercept s and y intercept Simplify your answers Type integers or fractions Use a comma to separate answers as needed Type each answer only once OB The graph has y intercept and no x intercept Simplify your answer Type an integer or a fraction OC The graph has x intercept s A and no y intercept Simplify your answer Type an integer or a fraction Use a comma to separate answers as needed Type each answer only once OD The graph has neither an x intercept nor a y intercept

1 Given U natural numbers from 1 to 20 P odd numbers less than 20 and Q multiples of 3 less than 20 a List the elements of i P ii Q b Find i P ii O iii PUQ iii PUQ iv PnQ iv POQ

For the function F x oblique asymptotes Ho a graph the rational function using transformations b use the final graph to find the domain and range and c use the final grap x 4 b The domain of the given function is 4 U 4 00 Type your answer in interval notation Use integers or fractions for any numbers in the expression The range of the given function is 0 00 Type your answer in interval notation Use integers or fractions for any numbers in the expression c What is are the vertical asymptote s Select the correct choice and if necessary fill in the answer box es to complete your choice There is one vertical asymptote It is x 4 Type an equation Use integers or fractions for any numbers in the equation B The left vertical asymptote is The right vertical asymptote is Type equations Use integers or fractions for any numbers in the equations COC OC There is no vertical asymptote What is are the horizontal asymptote s Select the correct choice and if necessary fill in the answer box es to complete your chce OA The top horizontal asymptote is The bottom horizontal asymptote is Type equations Use integers or fractions for any numbers in the equations OB There is one horizontal asymptote It is Type an equation Use integers or fractions for any numbers in the equation OC There is no horizontal asymptote E

x 1 Follow the steps for graphing a rational function to graph the function H x x 64 125 If needed first write the given function as a single rational expression Then factor the numerator and denominator of H x Select the correct choice complete your choice A H X x 5 x 5x 25 x 8 x 8 OB H x cannot be factored further What is the domain of H x 8 U 8 8 U 8 00 Simplify your answer Type your answer in interval notation Use integers or fractions for any numbers in the expression Write H x in lowest terms Select the correct choice and if necessary fill in the answer box to complete your choice COLLE Type your answer in factored form Do not simplify O A H x Simplify your answer OB H x is already in lowest terms

For the function F x oblique asymptotes A 1 Shift the graph of y 2 X 1 a graph the rational function using transformations b use the final graph to find the domain and range and c use a x 1 OB Shift the graph of y Choose the correct graph O A XN 1 D Shift the graph of y X Ay 2 1 C Shift the graph of y 1 unit left x 2 1 unit up 2 1 unit down 1 unit right b The domain of the given function is B Ay Q Q station Lice inteners or fractions for any numbers in the expression www O C 10 Q Q D G

Solve the inequality algebraically x 20 x 20 X 0 Move all terms to the left side of the inequality and then define the left side of the inequality as f x Then list the intervals determined by the r undefined Complete the following table Type your answers in interval notation Use ascending order Interval Sign What is the solution 20 Negative 20 0 Positive 0 20 Negative 20 00 Positive Simplify your answer Type your answer in interval notation Use integers or fractions for any numbers in the expression

oblique asymptotes Choose the correct graph O A TOT 10 10 O B 10 110 b The domain of the given function is 3 U 3 00 Type your answer in interval notation Use integers or fractions for any numbers in the expression OA There is one vertical asymptote It is Type an equation Use integers or fractions for any numbers in the equation OB The left vertical asymptote is The right vertical asymptote is frontions for any numbers in the equations O C 19 The range of the given function is 0 00 Type your answer in interval notation Use integers or fractions for any numbers in the expression c What is are the vertical asymptote s Select the correct choice and if necessary fill in the answer box es to complete your choice 10 and c use the final graph to lis D Ay Q G

Solve the inequality R x 0 where R x 6 x 2 6 4x 4 3x 6 by using the graph of the function I The solution set for R x 0 is Type your answer in interval notation

Solve the inequality algebraically x 20 x 20 X SO Interval Sign Move all terms to the left side of the inequality and then define the left side of the inequality as f x Then list the intervals determined by the real zeros undefined Complete the following table Type your answers in interval notation Use ascending order E

For the following demand function find E p and determine if demand is elastic or inelastic at the indicated price 600 q p 3 p 6 2 3 Type an integer or a simplified fraction Is the demand elastic or inelastic at p 6 E 6 O A Elastic because E p 1 OB Inelastic because E p 1 OC Inelastic because E p 1 OD Elastic because E p 1 G

f x 2x11x 11x 15x 9 Make sure to explain how you determined the significant characteristics of the function Those characteristics should include end behavior and x and y intercepts Answer Sel 40 30 20 10

Graph the function f x X in the standard viewing window of a calculator and trace from left to fight along a representative portion of the interval o 0 Then fill in the blank of the following sentence with either increasing or decreasing Over the interval specified this function is Graph the function Choose the correct graph below A B 10 10 AAALAALLPAALLLLILL 10 10 G 10 10 DINCELALL LLLLLL 10 Q 5 O C 10 10 Q 5 OD 10 10 10

A cup of hot coffee is placed on a counter and allowed to cool The temperature in degrees Celsius of the coffee t minutes after being placed on the counter is given by the accompanying function Complete parts a through d T t 28 48e 0 019t a What was the original temperature of the hot coffee How can the original temperature of the hot coffee be found Select the correct choice below and fill in the answer box to complete your choice OA Evaluate T OB Solve 28 48e 0 019t for t

Based on the ordered pairs seen in the table make a conjecture about whether the function f is even odd or neither even nor odd The function is odd odd neither even nor odd even BEX C because f x is equal to f x X 3 2 1 0 1 2 3 f x 10 5 4 0 4 5 10