Limits & Continuity Questions and Answers

21 1 mark The value of lim 10 2 10 a b abo a b is c 400 d 20 e t

Find all real zeros of the i Enter the real zeros sepa Question Help Messa

5 lim z 0 4z 2 z te N 2z e

The end of day values of a stock market index for the week of December 9 13 are graphed to the right where x is the day of the r On what day did the index show the greatest rate of increase On what day did it show the greatest rate of decrease Give the rates On what day did the index show the greatest rate of increase OA December 10 OB December 11 OC December 12

ections Solve each system of inequalities y 2 3 x 1 x 2

an object is given where t is measured in seconds Points of inflection occur at t 2 5 8 10 i Select all of the following intervals over which the object is speeding up 0 2 quad 2 5 quad 5 8 quad 8 10 quad 10 11 ii Select all of the following intervals over which the object is slowing down begin array IIIII 0 2 2 5 quad 5 8 8 10 10 11 end array

Use the Theorem on Limits of Rational Functions to find the limit If necessary state that the limit does not exist X 1 lim X 1 X 1 Select the correct choice below and fill in the answer box within your choice x 1 X 1 X 1 OB The limit does not exist OA lim Simplify your answer

Find the given limit lim x 4x 6 X 1 lim x 4x 6 Simplify your answer X 1

18 54 5 25 125 5 Consider the series a Write the series using summation notation b Determine if the series converges or diverges If the series converges find its 162 625

Fred bought a total of 12 books for 44 28 What was the mean cost of the books

What is the point of rotation for the cubic function f x x 4 3 5

2 Evaluate the following limits of sequences or explain why they do not exist a b c lim n lim n n n 2023 2n 17 sin 18n 19n 20 lim cos n 6n 7 3n n

40 1 tan x tan y cos x y COS X COS y

4 Consider the following piecewise function f x x 1 3 x 1 x 2 1 x 1 1 x 1 x 21 a Evaluate the piecewise function at the indicated values i f 1 ii f 0 b Graph the piecewisq function iii f 1 c What is the domain and range of the function Domain

The function f x 6x 4 e 6x has one critical number Find it X

Solve the inequality algebraically x 5 x x 6 x 7 x 1 0 List the intervals and sign in each interval Complete the following table Type your answers in interval notation Use ascending order Interval

Suppose f x x 8 where the domain of f equals 0 Find the following 16 Is f one to one 17 Formula of f 18 Domain of f 19 Bange f 1

3 Solve x x t e Atxo 4 1 0 do do A 3 3 1 2 2 x given that 1 is the only eigenvalue and express your result as 1

A table for f x is given below X f x X g x f x 3 A 4 5 Complete the following tables Hint Be sure to list the x values from least to greatest type your answer F type your answer 2 6 A F B G 0 B type your answer G type your answer 8 C H C type your answer H type your answer 2 10 D type your answer 1 type your answer 4 14 E type your answer J type your answer

A spoonful or medicine holds 10 mL How many spoonfuls of medicine would 2 bottles hold if each bottle holds 0 25 L

mtot datar f x W TV WN ww 4 2 3 3x 2

A truck averages 5 5 kilometres per litre of gasoline How many kilometres can the car go on 81 worth of fuel if fuel costs 1 08 per litre

River drove for 2 hours on the freeway They exited the freeway and decreased their speed by 20 miles per hour and drove for 2 more hours on a country road If their total trip was 212 miles then what was their speed on the freeway

X IL dx dy if R is the region outside the circle x y 1 and within the x y circle x 1 2 y 1

Show tan A B tanA tanB 1 tanAxtanB

Metric System The following scorecard shows the distance of a golf course Determine the distance to yards Hole 1 2 3 st 4 Black Blue Tees Tees 505 505 183 364 391 173 355 371 Handicap 3 15 11 7 Par 5344

b The equation of the line Note You can earn partial c Problem 9 1 point

On what interval s is t Note You can earn pa

Find limf x for the following graph X 0 2 0 O 1 Does not exist 7 2 f x x 1

D Question 6 4x 6 4x 6x Given f x asymptotes Determine the domain of f x and find 3 domain all real numbers except x 0 and x vertical asymptote x 0 3 domain all real numbers except x 2 2 3 2 vertical asymptotes x 0 andx domain all real numbers vertical asymptotes x 0 andx 312 3 Take Q 12

1 The inverse notation f used in a pure mathematics problem is following problem illustrates this idea

ASK YOUR TEACHER I PRACTICE ANOTHER nine whether the following relation represents y as a function of x

Match each exponential function to its grapl t x 5 2 x

C II x com Write the equation of this line in slope intercept form

L 26 A research team wishes to determine the altitude of a mountain as follows They use a laser light source at L mounted on a 2 meter pedestal to shine a light through the top of a pole P through the top of the mountain M The height of the pole is 20 meters The distance between the altitude of the mountain and the light is 1000 meters the distance between the pole and the light laser is 10 meters so the distance between the laser and the mountain is 1010 meters We assume right angles where they appear to be modeling assumptions Find the altitude of the mountain figures not drawn to scale light 2 m 10 m P pole 20 m 1000m M M mountain

Find the reference angle for the angle 205

The area of a square is 49 square inches or less Which set describes the domain for s the length of one side of the square

y x 2 12x 350 cluding the roots and the

For f x x and g x 6x 5 find the fo a fog b gof c fof

Study Cuide Find values of the function f n 4n 2 5n a f 0 b f 5 c f 5 d f p e f 2a f f 5 8 a f 0

x 25 Find the domain of the function f x 2 x 36 Select the correct choice below and if necessary fill in the O A The domain is x x x B O C Simplify your answer Use a comma to separate an The domain is x x x Simplify your answer Use a comma to separate an The domain is x x

where marbles ar randomly change direction At the bottom of the board are bins to catch the marbles 0 1 2 3 4 5 6 7 When a falling marble strikes a peg it will either bounce left or right Galton s motivation was to study the final distribution of marbles amongst the bins g How many total paths are there h Thinking of the number of paths to each bin and the total number of paths what are the probabilities of a marble landing in each bin Write as decimals

Question 9 ven the function f x 5x 7x d the Remainder Theorem 2 1 0 1 S 2

Identify the sampling method Then identify any bias in each method The student government wants to find out how many students study while listening to music A pollster interviews students selected at random as they leave the cafeteria at the end of fourth period Which sampling method is being used Select Which bias if any is present with this method Select Select If students have a different lunch period they are underrepresented by this sampling method The small sample size will cause the findings to be unreliable as a general conclusion There is no bias with this sampling method The students who have a different lunch period are overrepresented by this sampling methc

Find the open intervals where the function graphed below is a in decreasing 100 80 Ay

Find the exact value of each expression cos 13 4 b cos cos 3

or f x x 3 and g x x 3x 10 determine the domain of 2 X

2 Write a valid conclusion for each of the following arguments State the com mon valid argument form you use to create your conclusion If I do not wear my sunglasses then I can t drive I can drive Therefore I am hungry or I want a nap I am not hungry Therefore If you do not buy firewood then you will be cold If you are cold then

Find the exact value of each expression 35x 4 a sin 5 6 b sin n 357 sin 5 4 6

Fill in the blank to complete the trigonometric formula cos u v No Response