Limits & Continuity Questions and Answers

Find the equation of the graph given below Provide your answer below 3 2 0 0 1 3 TT 3 T TT 2TT 3 T 4TT 13 3 5TT 6TT

y cot 5x Drag the movable red point to set the asymptotes for one period of the given function Also place the blue point at the correct set of coordinates You may click on a point to verify its coordinates Provide your answer below TT 5 7 6 5 4 3 2 14 0 2 3 4 TT 5 2T 5 4TT 5 6m 5

a sec x 2 tar x 2 cox 2 cs x 2 a 5 Find the exact value of sin 26 cos 24 tan 24 10 sin 10 b cos p b tan o d in quadrant IV 3 5 in quadrant III 5 12 in quadrant IV

Find all of the following that applies then sketch the graph a Classify the type of conic section as a circle parabola ellipse or hyperbola b Center c Vertex or vertices d Focus or foci e Directrix parabola only f Eccentricity ellipse and hyperbola only g Sketch and label the graph 1 4x 9y 32x 36y 64 0

figure Provide your answer below A 0 TT 2 3 2 1 0 1 2 3 0 0 TT 2 Wild Value X does I X Choose the points in the

Higgst ne po Provide your answer below 2 311 2 TT 2 6 4 0 2 0 0 TT 2 m 3m 2 27 X ined in the interval 27 X 0

the origin with the given focus or directrix 1 Focus 6 0 2 Focus 0 4 3 Directrix x 3 4 Directrix y 5 5 Focus 0 7 6 Directrix x 9 7 Focus 1 0 8 Directrix x 1 9 Focus 2 0

The Maclaurin series of the function f x 4x sin 3x can be written as f x Cnxn n 0 where a few of the coefficients are C3 C4 C5 C6 C7 www

When writing a rational function as a power series if the numerator has degree one less than the denominator the partial fraction method will work True O False

2 15 pts Simplify the following cosx tanx COSX 1 sinx 3 15pts Evaluate cos 0 3 where cos0 3 4 with in 2th Quadrant and sin 5 7 wi B in Quadrant II 16 Find an equivalent expression for cot t

Find a power series for the function centered at c 5x x 3x g x I g x C 0 100 n 2 1 1 1 n 0 Determine the interval of convergence Enter your answer using interval notation 1 1

Use the power series 1 1 x to find a power h x h x 00 n 0 00 1 x Ixl 1 n 0 series for the function centered at 0 2 x 1 x 1 1 1 1 x 1 X Determine the interval of convergence Enter your answer using interval notation 1 1

Find the radius of convergence of the power series If you need to use co or co enter INFINITY or INFINITY respectively 1 n 0 n 9

Find the interval of convergence of the power series Be sure to include a check for convergence at the endpoints of the interval If the answer is an interval enter your answer using interval notation If the answer is a finite set of values enter your answers as a comma separated list of values 1 4x 1 n 1 n 1 11 11

State where the power series is centered nx n 0

sinx cos2x 1 Write your answer in radians in

On the graph of f x csc x and the interval 0 2 set the moving point to a value of x such that f x Provide your answer below 5 TT 2 1 11 11 1 TT 11 11 11 10 0 11 11 3TT 2 11 JE 11 THE 2TT 11 11 11 5TT 2

Given that csc x 9 29 what is csc x

Provide your answer below 4 2 O 2 and the interval 0 2 set x to a value such that f x I 1 9 10 0 1 1 TT 2TT

patient per hour now many milligrams of medication are delivered in 30 seconds Round to two decimal place Answer 2 A pediatric vitamin drug product contains the equivalent of 0 25 mg of fluoride ion in each milliliter How many milligrams of fluoride ion would be provided by a dropper that delivers 0 6 mL Round to two decimal place Answer 3 COLCRYS scored tablets each contain 0 6 mg of colchicine How many micrograms of colchicine would a patient take by administering one half tablet Round to the whole number Answer 4 An intravenous solution contains 500 g of a drug substance in each milliliter How many milligrams of the drug would a patient receive from the intravenous infusion of a liter of the solution Round to the whole number Answer

lim f x 0 x a lim g x 0 x a lim h x 1 x a lim p x x a lim q x x a evaluate if the following limits not are indeterminate forms If a limit is indeterminate enter INDETERMINATE a lim f x 9 x x a f b lim f x P x x a c lim h x P x x a d lim p x f x x a e lim p x 9 x x a lim x p x x a

For the data provided complete the following tasks a Apply both column and line sparklines to visualize the trends in the prices for each of the four stocks b Compute the daily change in the Dow Jones index and apply a win loss sparkline to visualize the daily up or down movement in the index Click the icon to view the closing stock prices Choose the correct column and line sparklines for GE O A Q Q OB Q O C Q Q 5 O D o 3 9 8 2010 4 9 9 2010 5 9 10 2010 6 9 13 2010 7 9 14 2010 8 9 15 2010 9 9 16 2010 10 9 17 2010 11 9 20 2010 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 126 08 126 36 127 99 129 61 128 85 129 43 129 67 130 19 131 79 17 9 18 17 97 18 56 18 74 18 72 18 97 18 81 18 93 20 64 20 61 20 62 21 26 21 45 21 59 21 93 21 86 21 75 15 7 15 91 15 98 16 25 16 16 16 34 16 23 16 29 16 55

Determine the number of terms required to approximate the sum of the convergent series with an error less than 0 001 1 1 6n n 1

Write an expression for the nth partial sum of the series Using the nth partial sum and the Definition of Convergence Divergence of a Series determine whether the series converges or diverges If convergent what is the sum of the series n 2 n Converges n

Find the nth term that generates the sequence then determine whether the sequence converges or diverges 1 8 27 64 25 50 75 100

Find the limit Use l Hospital s Rule where appropriate If there is a more elementary method consider using it 2x 8 X 4 lim X 4

Since the derivative of sin x is cos x and the derivative of 96x is 96 applying L Hospital s Rule a fourth time gives us the following sin x lim x 0 96x lim cos x X 0 96 Therefore we have the following 1 2x lim X 0 cos x 1 4x4 lim x 0 result sin x 16x X lim X 0 1 cos x 48x sin x lim x 0 96x lim X 0 cos x 96

Since the derivative of x sin x is 1 cos x and the derivative of 16x3 is 48x2 applying L Hospital s Rule a second time gives us the followin 1 cos x 48x lim x 0 x sin x 16x lim x 0 Analyzing this we see that as x 0 1 cos x and 48x

Since f x 8 sec x 1 and g x x sec x tan x applying L Hospital s Rule gives us the following f x lim x a g x lim x 0 lim x a g x 8 tan x x x tan x 8 sec x 1 lim x ot x sec x tan x Analyzing this we see that as x 0 8 sec x 1 and x sec x tan x

Since f x x sin x and g x 16x3 applying L Hospital s Rule gives us the following f x lim x a g x lim x 0 f x lim x a g x x 2 cos x 1 4x4 lim x sin x x 0 16x Analyzing this we see that as x 0 x sin x and 16x

As x 0 8 tan x x f and x tan x

We first rewrite the given limit such that we have a single rational expression as follows 8 lim x 0 X 8 tan x lim x 0 x tan x 022

The graph of the derivative f of a continuous function f is shown Assume f continues to 4 2 2 X y y f x 4 X 6 8 a On what interval s is f increasing Enter your answer in interval notation X X On what interval s is f decreasing Enter your answer in interval notation Your answer cannot be understood or graded More Information b At what value s of x does f have a local maximum Enter your answers as a comma separated list X At what value s of x does f have a local minimum Enter your answers as a comma separated list

What is the algebraic expre x x 5 Do not simplify

f x 14x 7 at 3 7 given point he equation of the tangent line to the graph of f x at the given point is

x 8 X 8 elect the correct choice below and if necessary fill in the answer box to complete your choice A The function f is discontinuous at x Use a comma to separate answers as needed B The function f is continuous for all x values

Determine if the function f x is continuous at the values x 5 and x 9 X 5 Is the function continuous at x 5 Yes Is the function continuous at x 9 O Yes O No O No

A cold metal bar at 80 C is submerged in a pool maintained at a temperature of 40 C After 55 seconds the temperature of the bar is 20 C How long will it take for the bar to attain a temperature of 30 C Use decimal notation Give your answer to one decimal place Round any intermediate calculations if needed to no less than four decimal places t seconds

Find the value of each variable The dot represents the center of the circle Lines that appear tangent are tangent a 50 a 880 m b O O CO

Use a reference angle to write sin Provide your answer below 31 36 in terms of the sine of a positive acute angle Include parentheses in your answer 31

REAL NUMBERS Finding the sale price without a calculator given the original pri The price of an item has been reduced by 65 The original price was 20 What is the price of the item now

Write and equivalent algebraic expression that involves x only tan sin 1 7 x

Use the product quotient and power rules of logarithms to rewrite the expression as a single logarithm 2 loga x 3 log y 5 loga z O loga x2y6 25 x2 loga y5 5 O x2y8 z5 x2y5 10Ba

A car dealership has 7 red 4 silver and 8 black cars on the lot Five cars are randomly selected to be displayed in front of the dealership Find the probability of selecting 2 red 2 black and 1 silver O 0 785 0 202 0 283 0 385 00117

Using synthetic division determine whether the numbers are zeros of the polynomial function 2 3 2 f x 3x 5x 6x 18 Select the correct choice below and if necessary fill in the answer boxes to complete your choice OA The number 3 is a zero of the polynomial function because f 3 OB Neither 3 nor 2 is a zero of the polynomial function because f 3 OC The number 3 is not a zero of the polynomial function because f 3 OD Both 3 and 2 are zeros of the polynomial function because f 3 0 and f 2 0 4 and the number 2 is not a zero of the polynomial function because f 2 and f 2 and the number 2 is a zero of the polynomial function because f 2

8 Sketch a possible graph of a function f showing any vertical asymptotes or holes and that satisfies all of the follow f 0 1 f 4 is undefined lim f x 1 18 lim f x lim f x DNE lim f x 88 lim f x co x 6

Does correlation imply causation in the amount of hamburgers chicken cooked on the grill and the amour of propane gas used on the grill

Write a polynomial f x that satisfies the given conditions 1 Polynomial of lowest degree with zeros of multiplicity 2 and multiplicity 1 and with 0 2 f 6 f x OC 2 3

The series Since 5 6n 7 the sequence the series then the series n 1 is most easily compared to 5 6n 7 5 6 72 5 6 7 v 5 6 12 and Select an answer 5 6 1 Select an answer by the Select an answer

Decide whether the series So Use a comparison test to a p series 1 k6 9k 5 k 1 k 1 converges diverges O 1 k6 9k 5 1 kp k converges where p