Limits & Continuity Questions and Answers

Given that the polynomial f x has 5 turning points which of the following most accurately describes the degree of f Select the correct answer below The degree of f x is at most 6 The degree of f x is at most 5 The degree of f x is at least 6 The degree of f x is at most 4 The degree of f x is at least 4 The degree of f x is at least 5

Given that tan 0 4 and 0 is in Quadrant III find sec 0 and sin 0 Provide your answer below

For the function I X CSC X set the moving point to a value of y a such that it is not a possible value of f x Provide your answer below 2 T 1 1 1 TT 5 2 95 0 1 F L T F 2TT

The graph of the function f x log7 x is stretched vertically by a factor of 6 reflected over the x axis reflected over th y axis and shifted down by 8 units Find the equation of the function g x described above Note If you are using log you need to type it in and use the subscript button on the keyboard There is no log button Provide your answer below g x

Using Descartes Rule of Signs write the greatest possible number of negative roots for the function g x 5x 7x 2x 2 holow

1 point Consider the system of differential equations Rewrite as Z a11 a12 921 922 Then det 911 921 x 912 922 2 and the eigenvalues are A A general solution is ciet 2 I 2 2 c e 21 x 2 x 1 x x 2 x 5 x2 1X

The function y e 5x is vertically stretched by a factor of 6 reflected across the y axis and then shifted up 1 units find the resulting function Provide your answer below

Determine the convergence or divergence of the series 2 1 m 13m2 Explain why to receive full credit Edit Format Table

Find the limit of the sequence an Ox 20

Divide using long division Write your answer in the form Q x given divisor Provide your R x D x 2x 6x 5 X 1 where Q x is the polynomial quotient R x is the remainder and D x is the

Divide 15x 12x 30x 24 by 5x 4 Provide your answer below

Find the measure of the least positive angle that is coterminal with the angle given Then find the measure of the negative angle that is nearest to and is coterminal with the angle given 51 The positive angle is

Which is an equation with a degree of 3 x intercepts located at 3 0 and 2 0 and a y intercept located at 0 0 Select the correct answer below O y x x 3 x 2 O y x x 3 x 2 Oy x 3 x 2 Oy x 3 x 2 Oy x 2 x 3

e a power series to approximate the area of the region with an error of less than 0 0001 Use a graphing utility to verify the result Round your answer to four decimal pla cos x dx 1 1 7 cos x dx 1 n 0 y 0 5 1 5 1 0 5 0 5 0 5 1 1 5

Consider flipping a coin five times How many outcomes are possible 4 Let F obtain at least one head in five flips of a coin What does the event F represent P F obtain Select heads in five flips of a coin Find P F Find P F the probability of obtaining at least one head in five flips of a coin Enter the probability as a fraction

Consider a bowl containing 120 marbles 20 green 18 blue 20 gray 7 orange 4 yellow 21 cat eyes and 30 multicolored Suppose each marble has an equal chance of being picked from the Find the following probabilities Round your answers to three decimal places a P gray b P cat eye c P multicolored

Player Babe Ruth Willie Mays Ty Cobb Walter Johnson Hank Aaron Is the rank a function of the player name Is the player name a function of the rank Select the correct answer below Rank 1 2 3 4 5 Rank is a function of player name but player name is NOT a function of rank Rank is NOT a function of player name but player name is a function of rank Rank is NOT a function of player name AND player name is NOT a function of rank Rank is a function of player name AND player name is a function of rank

Identify the expression below as a monomial binomial or trinomial 6x 8 Select the correct answer below Monomial Binomial Trinomial

Which of the following are trinomials Select all correct answers Select all that apply 3pq 2p 2p qr 3p q 3pqr 3p 2p q C 2 S 2pg 3pgr

Find the leading coefficient of the following polynomial 5 x 3x x4

Find the zeroes of the following polynomial f x x 4x Provide your answer below 21x List the zeroes separated by commas For example if you found that the zeroes were x 1 x 2 and x 3 you wou enter 1 2 3

Select the correct answer below 7654321 6 5 4 7 6 5 4 3 2 11 2 EL 2 127 4567 4 5 6 7 T 2 3 4 5 6 7 x 4 with multiplicity 1 x 4 with multiplicity 1 and x 1 with multiplicity 2 x 4 with multiplicity 1 x 4 with multiplicity 2 and x 1 with multiplicity 1 x 4 with multiplicity 2 x 4 with multiplicity 1 and x 1 with multiplicity 1 Ox 4 with multiplicity 1 x 4 with multiplicity 2 and x 1 with multiplicity 1

3 3 47 3 3 find det A Given the matrix A 4 4 3 1 2

Determine if matrix A given below is invertible Select the correct answer below Matrix A is invertible Matrix A is not invertible A 6 3 6 5 1 1 2 1 5

4n Determine whether m is convergent or divergent Use only methods taught in this 5n 1 class 4n tor divergent Ilse only methods taught in this

Find a power series representation for the function and find I the interval of convergence Use only methods taught in this class f x 8 9 x

Find Sin z 01 1 sin z sin z 1 sin z COS 2 1 sin z points 0006 z 1 sin

Find the derivative y for each curve functice y 2x5 In x 4

You do not need to show work for this question 5 4 3 2 0 2 a List all intervals on which f is increasing b List all r values where f has a local minimum fr c Is f concave up or concave down on 1 x 1 d List all x values where f is not continuous f Is the value of 2 e What is the absolute maximum value of f on 0 4 S z da positive or negative 3 answer to each of th

Since u x 30 then converting back to an expression in x we get the following 23 0 23 2 C 9

If u x 30 is substituted into We must also convert x dx into an expression involving u We know that du x x 30 dx then we have 3x dx so x dx e x x 1 2 dx u x dx du

all the local maxima local minima and saddle points of the given function f x y x xy y 3x 3y 6 Select the correct choice below and fill in any answer boxes within your choice OA There are local maxima located at Simplify your answers Type ordered pairs Use a comma to separate answers as needed OB There are no local maxima Select the correct choice below and fill in any answer boxes within your choice OA There are local minima located at Simplify your answers Type ordered pairs Use a comma to separate answers as needed OB There are no local minima Sele e correct choice below and fill in any answer boxes within your choice OA There are saddle points located at Simplify your answers Type ordered pairs Use a comma to separate answers as needed OB There are no saddle points

Tarot cards are used for telling fortunes and in a reading the arrangement of the cards is as important as the cards themselves How ma different readings are possible if three cards are selected from a set of seven Tarot cards readings

Let g x f t dt The graph of y f t is given below 5 4 3 2 1 1 2 3 4 5 3 4 5 6 7 8 9 10 Determine the open interval s on which g is decreasing Enter the solution using interval notation Enter DNE if g is decreasing over no interval Determine the open interval s on which g is increasing Enter the solution using interval notation Enter DNE if g is increasing over no interval Determine the location x value of any local minimum of g over 0 10 OH Og has no relative minimum Determine the location x value of any local maximum of g over 0 10 0x og has no relative maximum

QUESTION 10 3pts Consider defined by f x Find the value of k such that f is continuous 1 9 if r 3 3 ek 1 if I 3

Evaluate the integral S tan 10x sec 10x dx tan 10x sec 10x dx

Show every step of the process of evaluating the integral below Be sure to but a box around the answer in your hand written work Then indicate the technique s used Select all choices that apply 11 x dx O Improper Integral O Integration by Parts O Logarithmic Integration

Dertermine whether each of the following Converge or Diverge a 3n 2n n 1 8 n b n 0 Which of the following multiple choice answers best applies to the series in part c The series in part c converges conditionally O The series in part c diverges O The series in part c converges absolutely C 221 n 1 1 n 1

For the given conic section determine each of the following a the type of conic section b the center if applicable c the focus or foci d the vertex or vertices e the eccentricity Which of the choices below is the correct type of conic section for the equation above O Ellipse O Circle 9x 4y 36x 24y 36 0 Parabola O Hyperbola Degenerate Conic

Question 3 2 2 4 points Compute the following limits or else prove that they do not exist using methods from algebra and Calculus You must justify your steps with reference to theorems or definitions learned in class correctly and legibly and use correct notation to earn full credit 14 2r 2x 4 a lim

Test the series for convergence or divergence 1 7n 1 5n 1 n 1 Evaluate the following limit If the quantity diverges enter DIVERGES lim 1 318 Since lim 1 818 Need Help 7n 1 5n 1 7n 1 5n 1 Master it Select Select exists and does not equal 0 Select

5 12 Consider the rational function r x Evaluate the local behavior As x 1 r x As x 1 r x As x 2 r x As x 2 r x As x 4 r x As x 4 r x 750 x 1 7x 3 x 1 x 1 x 4 x 2

A 11 2 resistor and a variable resistor of resistance R are placed in parallel The expression for the resulting resistance RT is given by RT value of RT as R o The limiting value of R is Simplify your answer 11R 11 R Determ

8 Solve 2 logw 7 logw log w 10 0 Hint simplify the question by replacing the variable

6 As a tornado moves its speed increases The function S d 93 log d 65 relates the speed of the wind S in miles per hour near the center of a tornado to the distance that the tornado has travelled d in miles Determine the distance that a tornado has travelled if the speed of the wind at the center of the tornado reaches 150 miles per hour 3 marks

a log4 log 10 000 log 32 4 marks

d Determine the remainder when f x x 3x x 5 is divided by x 2 3 marks

In our series 9 10 100 9 1000 81 the ratio 1000 81 100 9 is r

Find 10 partial sums of the series Round your answers to five decimal places n 1 n 25 4 1 2 3 4 5 6 7 7 Sn

Therefore we have the following If an answer does not exist enter DNE 6n lim 24 1 2 60 II lim eln y n