Limits & Continuity Questions and Answers

15 Evaluate log2 15 What is the answer a 3537 b 2 8272 c 2559 d 3 9073

1 Solve for x 3 81 a 4 b 2 c 3 d 5

45 Evaluate the following expressions Your answer must be an exact angle in radians and in the interval 0 Example Enter pi 6 for 6 a cos 1 b cos 2 2 c cos 1 E

Fill in the blanks 1 If tan z 1 5 then tan x 2 If sin x 0 7 then sin x 3 If cos x 0 5 then cos x 4 If tan x 1 5 then tan x

In 1 2 circle the letter of the correct answer 1 Solve for all values of x where 0 x 2 tan 2x 3 a x 7t b x x 2 27 1 20

Given the equation y 8 sin The amplitude is The period is The horizontal shift is The midline is y 4T x 8TT 3 5 units to the Select an answer

Identify whether the following equation is an identity a 1 ax 1 a 1

Adding Vectors c i 2j d 2i 2j 3 c d Do not put any spaces between the numbers and the symbols

K Find an equation in poi 4 2 and 1 3 What is the equation of Use integers or simplit

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quation in point slope y y m x 6 and 2 1

Find the point of intersection of the y 1 3 1 x 12 The point of intersection is T

Consider four consecutive integers p q r s The product of the inner two integers will always be more than the product of the outer two integers The difference qr ps a is the same for any four consecutive integers ar p s Find the value of this constant difference

eck e the system by graphing 3x 2y 12 6x 4y 24 the graphing tool to graph the system Question 6 4 1 15 Part 2 of 2 The unique solution is ct the correct choice below and fill in any answer boxes present in your cho

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e substitution method 3 61 Questi solution of the system Select the correct cho unique solution to the system is Type an re are an infinite number of solutions

Check Solve by using substitution or elimination b 5x 4y 5 10x 8y 10 Select the correct choice below and fill in a

ring 34 Write an equ Vertical asym x intercepts a Horizontal as

Use L Hospital to determine the following limit Use exact value In x 7lna x im 1

Evaluate the limit using L Hopital s rule 2x e6x lim X18 1 9 X

Suppose f 5 0 f 5 2 g 5 0 g 5 2 and all functions are continuous f x lim x 5 g x

In which limits below can we use L Hospital s Rule sin 5x 5x Olim x 0 Olim x 0 sin 2x x 2 2x Olim x tan x sin x 5x x 0 cotx Olim

A one to one function is given Write an equation for the inverse function n x 7x 2 Tersay

q x U x 1 3 SYA ANGE INTE LE HE 15 512 EVLET SER E VIVE 2015 ETEEN 672 SOULTRAPERARY TREERTES More or line bregunte TERMIN BETER OM THE BUCARES INTE 22 TOANS CENTER WENGER A 306 MODS S g x 6 x 9 CEVORED 1987 A one to one function is given Write an equation for the inverse function

A 75 B 7 2 Above is the graph of the function f x with five points on the graph labeled Using the graph and only the labeled points determine the following E Note There may be more than one correct answer to the following but only one point should be given as the answer If none of the points satisfy the conditions then say none 1 A point where f x is increasing 2 A point where f x is increasing 3 The point where f x is the largest 4 The point where f x is the smallest 5 A point where the instantaneous rate of change of f x is zero 6 A point for which f x is positive

Evaluate the limit lim x 5 x 7 x 1 448 O 1286 O 1306 1296 320

1 Evaluate the Riemann sum for f x 3 1 1 x 2 x 14 with six subintervals taking the sample points to be left endpoints Explain with the aid of a diagram what the Riemann sum represents

a Po lal B sin COS tan 7 4 1 0 8 9 5 6 2 3 ans 1 X 1 a b 1 x The angle of elevation to the top of a Building in New York is found to be 10 degrees from the ground at a distance of 1 mile from the base of the building Using this information find the height of the building Round to the tenths Hint 1 mile 5280 feet

Find the limit of the series n 1 1 17x 3 2 2n

Sin COS tan Simplify 0 tan t sec t cos t ans 1 L to a single trig function with no fractions

Simplify the complex fraction I point n 3 n 2 6n 8 n 1 n 2

Which of the following graphs represent the function fx 3x 5 and the graph of it inverse 5 At 24 3 4 3 2 4 3 23 9 1 2 1 2 3 4 1 2 3 4 5

1 Tina had this last question to solv Logic She promises to bake a pie fo instructor gives her this problem to s There are three mistakes in this state

1 True or False log a p The value of a must be positive T or F The value of b must be positive Tor F The value of p must be positive Tor F

Let f be the function defined by f x x 1 for 0 x 3 for 3 x 5 Suppose the function gis defined by g x k x 1 for 0 x 3 mx 2 for 3 x 5 where k and mare constants If g is differentiable at x 3 what are the values of kand m

Evaluate the limit lim 818 11x 8x 2 2x 8

Let X represent the full height of a certain species of tree Assume that X has a normal probability distribution with mean 100 1 ft and standard deviation 49 5 ft You intend to measure a random sample of n 19 trees The bell curve below represents the distribution of these sample means The scale on the horizontal axis is the standard error standa deviation of the sampling distribution Complete the indicated boxes correct to two decimal places Hi 6 0

Mortgages In a random sample of 18 months from January 2011 through December 2020 the mean interest rate for 30 year fixed rate home mortgages was 3 95 and the standard deviation was 0 49 Assume the interest rates are normally distributed Source Freddie Mac

21 What is the period of the graph of y sin2x2 A 4T B C 71

36 Construct one period of the graph of the equation y sin x 6 Start at x 0 A n fo B C D 211 2TT MA 2TT

40 Evaluate 2 sin 67 5 cos 67 5 What is the second step equal to A sin 2 67 5 B cos 87 5 67 5 2 C cos 2 67 5 67 5 2 D sin

31 Find the solution set of each equation in the interval 0 x 2 sin x csc x 2 0 A T B 3TT 22 C 0 D 0

13 Evaluate sin 54 cos 9 cos 54 sin 9 What is the value A 2 B 2 C 0 8910 D 0 4540

3 Find the solution set of each equation in the interval 0 sx 2 tanx 1 0 A 157 B 37 77 C 7 I D 3m 5m

2 Construct one period of the graph of the equation y cot x Start at x 0 A B D

A rigid block of mass M is supported by three symmetrically spaced rods as shown in figure Each copper rod has an area of 750 mm 2 E 120 GPa and the allowable stress is 75 MPa The steel rod has an area of 1100 mm 2 E 200 GPa and the allowable stress is 150 MPa Determine the largest mass M which can be supported Copper 145 mm A 12 857 23 kg B 25 800 kg C 21 629 71 kg D 15 900 kg M Steel 200 mm Copper 145 mm

Let vk k 1 be an arithmetic sequence such that v1 3 Find the integer n and the common difference d so that vn 6 and Sn v1 V2 vn vn 28 5

11 How many different 5 member student committees can be formed from a group of candidates 53 130 12 Kyle has 6 favorite books If he wishes to take 4 books on a road trip how many different combinations of 4 books are possible 360

Plot the point where 0 Q Clear All Draw 57 3

In a circle of radius 2 miles the length of the arc that subtends a central angle of 4 radians is miles