Limits & Continuity Questions and Answers

23 Breeding rabbits Fibonacci posed the following problem Suppose that rabbits live forever and that every month each pair produces a new pair which becomes reproductive at age 2 months If we start with one newborn pair how many pairs of rabbits will we have in the nth month Show that the answer is F the nth term of the Fibonacci sequence defined in Example 4

2 Sketch the graph of a function f x that satisfies all the following conditions f x is defined for all values of x except for x 0 f 2 2 f 2 1 lim f x 0 X118 lim f x 0 X 0 lim f x 3 X 2 lim f x 1 X 2 lim f x 0 x 00 lim f x 0 x 2

The limit represents f c for a function f x and a number c Find f x and c 82 2 Ax 4 Ax C lim Ax 0

Which molecule is NOT hypervalent Select the correct answer below OSF6 OPBr3 OPBr5 O XeF6 0

Find the constants a and b such that the function is continuous on the entire real line 7 f x ax b 7 a b x 2 2 x 5 x 25

Listen Use the definition of the derivative to determine f x for f x x5 Determine the domain of f x and f x Of x 5x4 R R f x 5x R R x x R R Of x 5x4 R R x x R R

Find the surface area of revolution about the x axis of y 7 3 over the interval 1 x 3

27 Convert to a decimal Round to 3 decimal places if necessary 71 8 17

Find the quotient Round to 3 decimal places 45 0 282

4 Find the quotient Round to 3 decimal places 59 0 001

Solve 1 179 0 05 0 121 0 482 0 000

Problems will receive a grade for completeness not accuracy To receive the points for any assignment students MUST show their work Problem can be completed multiple ways on paper then photographed and uploaded into the corresponding Dropbox in Excel or in Word If homework is completed in Excel work doesn t need to be typed out if the functions can be viewed in the formula bar Once problems are completed the answer key will be given for the completed problems If a student needs assistance with a specific problem they should post a request in the Questions Comments Discussion for the corresponding chapter then a similar problem will be reviewed Due to time constraints actual homework problems will not be reviewed in class If an assignment contains multiple photos files submit the pictures files using an app program that compiles all of the pictures into 1 file Some cell phones have software that can combine the photos but students can also use the FREE Adobe scan app Chapter 1 3 pts Compare and contrast each business form by marking the appropriate business form Creation Number Easier to More Greater Owners government liable for exit end Owners involvement company maintenance of easier funding sources Sole proprietorship Partnership Limited liability comp LLC S corporation C corporation Taxation greater Chapter 2 2 pts Match each of the following transactions events to the accounting principle considered in recording them a Business entity principle b Objectivity principle c Cost principle d Going concern principle e Monetary unit principle f Revenue recognition principle g Materiality principle 1 An insurance company receives insurance premiums for six future months worth of coverage 2 Helen Cho a sole proprietor pays for her daughter s preschool out of business funds 3 A company expensed a 20 wastebasket in the year it is acquired instead of depreciating it over its useful life of 10 years 4 Helen added several thousand dollars to the Equipment account that she believed was undervalued 5 A building is for sale at 480 000 An appraisal is given for 450 000

4 Please write as a decimal 2 10

What is the range of the function y 3 x 8 O y O 8 y O 0 y

valuate the integral Use C for any needed constant In x x da

Let u 6 5 and v 2 3 Express u v in the form a b u v Simplify your answers

Use the Evaluation Theorem to decide if the definite integral exists and either evaluate the integral or enter DNE if it does not exist 22 5 dz

49 Name the quadrant or quadrants where the terminal side of an angle in standard position may be located to satisfy the given conditions sin 8 0 and tan 0 0 O A III B IV O C II D II and III

41 Fill in the blank parentheses with the trigonometric function that makes the given equation a true statement cot e 1 A tane B sece C csce D cose

Consider the n term sum b 11 a For every positive integer n find b and f x such that f 7 11 and R is a right Riemann sum for the definite integral f x dx C f x sqrt 11 abs x 7 4 2 b For every positive integer n find c and g x such that g 11 11 and R is a right Riemann sum for the definite integral 9 x dx 15 8 2 4 4 R 1 11 n g x 4n Optional question Evaluate T lim R

3 Given the function f x In x state the equation for the following translations and or reflections a f reflected about the x axis and shifted 2 units left b f reflected about the y axis and shifted 6 units up c stretched vertically by a factor of 5 and shifted 3 units right

Starting with the graph of f z 9 write the equation of the graph that results when a f z is shifted 8 units downward y b f z is shifted 3 units to the right y c f x is reflected about the x axis and the y axis y

For each slope below enter the value correct to four decimal places f x f x1 X2X1 Let f x 2 ln x Using the formula m of f x that connects the points 1 3 and x2 8 m x2 5 m x2 4 m x2 3 1 m 3 find the slope of the secant line on the gr

Write 4loga 5log x 1 4log x 1 as a single logarithm Assume all arguments represent positive numbers

37634 9 6 bu A 1 4 145 5 ya d What is the least possible degree of the polynomial graphed abov Question Help Video

Evaluate the limit if it exists Use symbolic notation and fractions where needed Enter DNE if the limit does not exist lim 2 sec 0 2 tan 0

Evaluate the limit Use symbolic notation and fractions where needed lim 1 cos 5h h II

Find all solutions of the equation and express them in the form a bi Enter your answers as a comma separated list Simplify your answer completel 2x 2x 1 0 X 1 i 1 i 2

Let h be a function defined for all real numbers except for 1 x 5 x 1 Also let h the derivative of h be defined as h x On which intervals is h increasing Choose 1 answer B 5 and 1 00 5 1 and 1 00 5 1 only 5 only The entire domain of h

If 15 f x 17 then f a da Find the best lower and upper bounds poss

To find he domain of the function g x x 3x2 9 we need to factor numerator and denominator first then simplify the common factor s and then find the domain True False

2 a State lim 0 0 b Find lim x 0 sin 0 0 sin 2x X sin 2x Find lim x 0 sin 3x sin 3x lim x 0 X 9229307 laulance amoe werb on einmasse bus athen to sonsolingie od to gribasdzrobno amet bine noitation upinde sinquiqga mos guia volupobeastsmodium notiv zuwl son ensihog ind gilenoisonul 2 101ginalna apa adil and lim and lim x 0 sin nx x 0 sin mx sin nx X mil hins Eudaliva om to helword isitmin edetesoras juo vud of eigmoita tezat snitor amor grimmorisq raras anivloz moldong san o tomonta no assen 8507 150 aw in ton sob ambo agbelwond ball eshententoma

L Use the definition to prove that the limit is L Given 0 assume f x L then x 7 1 1 lim x 7 X 4 2 2 X Let 8 28 S 1 3 X 2 X X If 0 x X 1 1 2 X E E E 2 when 8 2 you have 2 E

Consider the function f x x and the point P 4 2 on the graph 7 a Graph fand the secant lines passing through the point P 4 2 and Q x f x for x values of 1 5 and 8 Find the slope of each secant line Round your answers to three decimal places line passing through Q 1 f x line passing through Q 5 f x line passing through Q 8 f x b Use the results of part b to estimate the slope of the tangent line to the graph of fat P 4 2 Describe how to improve your approximation of the slope Choose secant lines that are nearly horizontal Define the secant lines with points farther away from P Ochoose secant lines that are nearly vertical Define the secant lines with points closer to P

Give a geometric description of the following set of points x y 2 12x 16y 8z 52 0 Select the correct choice below and fill in the answer boxes within your choice Simplify your answers OA A ball centered at with radius OB B The exterior of a ball centered at with radius OC A sphere centered at with radius

Find the equation of the sphere passing through P 4 5 4 and Q 2 1 3 with its center at the midpoint of PQ The standard equation of the sphere is x 1 y 2 Z Simplify your answer 7 2 71 4

Determine the following limit 35x 4x 4x lim 3 X 42x x 5x 2 2 Select the correct choice below and if necessary fill in the answer box to comp O A lim 3 4x 4x 35x Simplify your answer 3 2 x 42x x 5x 2 OB The limit as x approaches o does not exist and is neither nor

Estimate the limit lim3 numerically or state that the limit does not exist Use decimal notation Give your answers to four decimal places Use the symbol co for infinity Enter DNE into the answer field if the limit does not exist f 3 1 f 3 01 f 3 001 x 8 lim x 3 x 9 11 x 8 x 9

1 point What are the rectangular coordinates of the point whose spherical coordinates are 2 1 1 y Z

Evaluate SSB f x y z dV for the specified function f and B f x y z SB f x y z dV N X 2 x 4 0 y 7 0 z 4

Note If there is more than one numerical answer separate them with commas If the answer is an interval enter it in the form a b a b a b or a b Write infinity for and infinity for o Click here for more help on entering intervals The domain of y 8 x is the interval infinity 8 Entered Answer Preview Fo preview answers

Evaluate the limit using the Basic Limit Laws and the limits limx xpl Give your answer as a whole number lim x x 14 11 la and limck k

under the given curve by dividing the indicated intervals into n subintervals and then add up the areas of the inscribed rectangles f x 4 x 3 5 text from x 1 text to x 4 n 5 n 10

A sum of scalar multiples of two vectors such as au bv where a and b are scalars is called a linear combination of the vecto Let u 3 3 and v 3 3 Express 3 21 as a linear combination of u and v 3 21 u v

x y x 5 No Solution 10 9 8 7 6 5 4 3 2 1 10 9 8 6 5 4 3 2 1 1 2 3 375 4 5 1917 6 7 1 do 8 9 10 2 7 8 9 10 Clear All Fill Graph Layer Point 1 Point 4 Line 2

f x x 2 On which intervals is the graph of f concave down Choose 1 answer A B C D 2 only x 2 only x 2 only 2 only

8 In 1 x and and 1 x n 0 G X Starting from identity determine taylor series f around c 0 that is maclauein series of f yet

9 lim x 0 2 X 1 e sin x 2 x 1 e

Find all zeros of the function f a 162 1042 125 25 Enter the zeros as fractions or integers separated by commas

Evaluate if possible the six trigonometric functions at the real number If an answer is undefined enter UNDEFINED 2x 3 sin t cost tant 3 X X csc t sect cott 3 3 x x