Limits & Continuity Questions and Answers

Listen Determine the limitlim x 14 14 x O 14 2 0 14 14 O 14 28 Odne

Determine the limit lim x 9 x 19 9 Oo Odne O 18 Question 8 0 5 points Listen

The lengths of the sides of a triangle are given Determine whether the triangle is a right triangle 12 15 18 Yes No

In the given right triangle find the side labeled x X X 90 72

Listen How close to 1 do we have to take x so that 1 5 01 25 1 125 O 1 5 O 1 25 Question 9 0 45 points 1 1 x 125

Listen Determine the value for to provelim 2 6 5 x 2 08 2 08 E 08 2 1 2 08 The limit dne

State the value of lim fx 2 x 0 8 O 1 4 1 4 does not exist Question 2 0 5 points f x if it exists fx 3 x x 4 x x

This problem is modeled on the example worked in 3 1 of Lomax Hahs Vaughn Use this small data set Please find Please find 8 2 X 6 i 1 X 7 Please find X E i 5 X 8 X5 8 X 4 X6 1 X3 2 X7 3 X4 6 X8 2

Find the value of x for which m n The value of x for which m n is m 4x 27

a The graph of y g x is shown Draw the graph of y g 2x 1 6 8 6 tr A 6 X b The graph of y h x is shown Draw the graph of y h x 4 F 6 2 2

Use the remainder theorem to find P 3 for P x x 4x 3x 7 Specifically give the quotient and the remainder for the associated division and the value of P 3 Quotient 0 Remainder P 3 0 0 8 X 00 3

Suppose that the polynomial function fis defined as follows f x 5x x 12 x 11 x 8 List each zero of f according to its multiplicity in the categories below If there is more than one answer for a multiplicity separate them with commas If there is no answer click on Nor 0 Zero s of multiplicity two 0 Zero s of multiplicity three 0 Zero s of multiplicity one X 00 None

Let q x x 6x 96x 7 Find all values of a for which q x 0 x Enter your response as a comma separated list of numbers Verify your result by plotting the graph of g x

Evaluate the limit If the limit does not exist type DNE lim 3 h 9 h 0

Use the Fundamental Theorem of Calculus to find the derivative of F x 5 F x sin t5 dt

Use synthetic division to find the quotient and remainder when 2x a Complete this synthetic division table 3 2 6 7 0 0 1 b Write your answer in the following form Quotient 2x 2 6x 3 x 3 x 3 6x 3 is divided by x 3 by completing the parts below Remainder x 3 X

An experimental serum was injected into 500 guinea pigs Initially 150 of the guinea pigs had circular cells 250 had elliptical cells and 100 had irregular cells After the serum was injected all of the guinea pigs with circular cells were affected 200 with elliptical cells were affected and none of those with irregular cells were affected Determine the empirical probability that a guinea pig with a circular cells b elliptical cells and c irregular cells will be affected b injection of serum a The empirical probability that a guinea pig with circular cells will be affected by injection of the serum is Type an integer or a simplified fraction b The empirical probability that a guinea pig with elliptical cells will be affected by injection of the serum is Type an integer or a simplified fraction c The empirical probability that a guinea pig with irregular cells will be affected by injection of the serum is W Type an integer or a simplified fraction

Complete the table y y 0 3 1 2 y y 0 3 HDX CN Simplify you

Your favorite math teacher abacus that Albert Einstein received for his 16th birthday for 1 000 Each year it appreciates in value by 5 Which equation can be used to find the value v of the abacus x years after it was purchased a v 1895 1 05 b v 1000 95 OA OD c V 1000 1 05 d v 1000 1 05

Round all decimal answers correctly to THREE decimal places D Question 1 log7 3 log7 x log7 32 1 pts

Translate to an algebraic expression 49 more than n The translation is

Evaluate the formula A P 1 rt for the quantity requested Find A if P 3000 r 6 and t 3 yr A S Simplify your answer www

There is a rack of 12 billiard balls Balls numbered 1 through 8 are solid colored Balls nun 12 contain stripes If one ball is selected at random determine the odds for it being striped The odds are 1 3 Type whole numbers Simplify your answer

Evaluate the formula for the given quantity 5 C F 32 Find C when F 40 40 degrees Fahrenheit is equal to www degrees Celsius

Evaluate 9 013x for x 4 When x 4 9 013x

For the wheel pictured on the right assume that a person spins the pointer and is awarded the amount indicated by the pointer If it costs 5 to play the game determine a the expectation of a person who plays the game and b the fair price to play the game a What is the expectation 0 5 b What is the fair price to play the game

Write the equation in exponential form 1 log 273 3 www The equation in exponential form is Type an equation Use integers or fractions for any numbers in the equa

Find the numerical value of the expression if x 2 10x 3 3x The numerical value of the expression is

Find the numerical value for m 8 When m 12 4 Simplify fractions if necessary when m 12

A card is picked from a standard deck of 52 cards Determine the odds against and the face card king queen or jack The odds against selecting a face card are Type integers or decimals

Use the following statement to answer parts a and b Two hundred raffle tickets are sold for 3 each One prize of 400 is to be awarded Winners do not have their ticket costs of 3 refunded to them Raul purchases one ticket a Determine his expected value b Determine the fair price of a ticket a His expected value is Type an integer or a decimal

Find the indicated value of the function Use your calculator to approximate irrational numbers Round irrationa numbers to the nearest thousandth g x 68 12x g 6 g 6 Type an integer or decimal rounded to the nearest thousandth as needed

Solve the following equation for t 1 S gtx 10 10 sg 10 sg g 9 Type exact answers using radicals as needed Use a comma to separate answers as needed Ration denominators t 12 Co

Solve by using the square root property of equality 5k 1 12 Choose the answer that represents all solutions of 5k 1 12 A 11 5 B 4 or 11 5 1 2 3 5 OC 2 3 1 or or 1 2 3 5 2 3 1 5

5 x 3 1 g x 1 3 x 2 I 1 g x 2 x 2 54 3 2 1 Find f 3 5 4 3 2 1 9 0 1 2 3 1 N 3 4 5 1 2 h x 5 54 3 2 1 Find f 2 4 x 2 2 x 5 5 4 3 2 1 d 0 1 2 3 2 3 for 4 5

Fill in the blank with an appropriat A controlled operation that yields a set of results is called a n A controlled operation that yields a set of results is called a n experiment theoretical probability empirical probability outcome

4a 6a 6 4a 6a 6 Simplify your answer Type exponential notation with positive exponents

3x x 5 x 12x 5x 2x3 ts Evaluate the limit lim

Verify the identity cos a sin x 11 L 503 sin a II III 1 sin x 1 cos a cos a 1 cos a sin a 1 cos a P cos x sin a 1 cos a 1 cos x x sin a 1 cos x sin x sin 2 1 cos a

Graph fand g in the same viewing rectangle f x 7 cos x 7 sin x g x 7 14 sin x Do the graphs suggest that the equation f x g x is an identity Yes No Prove your answer f x 7 cos x 7 sin x 7 cos x 7 sin x 7 sin x 7 g x Thus we can conclude the following Since f x g x for some x this is not an identity Ciproflx g x for all x this is an identity

Verify the identity 1 cos B 1 cos Expand the product and then use a Use a Reciprocal Identity 1 csc 6 Pythagorean Identity 1 cos 5 1 cos 3 1 cos B 2 sin B 1 csc B X

Verify the identity cos 4 1 sin A tan A sec A

Verify the identity 8 cos x 4 4 8 sin x 8 cos x 4 81 100 w 48 sin x 4 4

The graph of a function is given y 5 3 1 5 a Determine the net change between the indicated points on the graph 1 2 X b Determine the average rate of change between the indicated points on the graph 1 2

Indicate whether 37 is prime or composite Is 37 prime or composite O Composite O Prime

If the odds against an event are 5 9 then the probability that the event wil The probability is Type an integer or a simplified fraction

Find the prime factorization of the following number 42 The prime factorization of 42 is

Decide what number must be added to make the exp x2 0 4x What number must be added to make the expression a perfect square trinomial x2 0 4x 0 04 Type an integer or a decimal Factor the trinomial 2 Use integers or decimals for any numbers in the expression

O Consider the mathematical system defined by the following table Answer parts a through g T D M B T D B T D D B T D M M B T D D M M B B T B Inere is no identity element c For each element in the set give the corresponding inverse element if it exists Start with T Select the correct choice below and if necessary fill in the answer box to complete your c OA The inverse element that corresponds to T is OB Thas no inverse element Now determine the inverse element of D Select the correct choice below and if necessary fill in the answer box to complete your choice QA The inverse element that corresponds to D is OB D has no inverse element Now determine the inverse element of M Select the correct choice below and if necessary fill in the answer box to complete your choice

On a die the sum of the dots on the opposite faces is seven Two six sided dice are placed together on top of one another on a table as shown in the figure below The top and bottom faces of the bottom die and the bottom face of the top die cannot be seen If you walk around the table what is the sum of all the dots on all the visible faces of the dice The sum of all the dots on all the visible faces of the dice is dots