Limits & Continuity Questions and Answers

14 If sin A sin B and angles A and B are acute angles what is the value of cos A B 13 a 0 12 65 I

13 Find tan arccos a 1 b 3 C 1 d A 4 I

20 Solve the triangle a B 89 a 14 c 20 b B 139 a 7 b 8 c B 139 a 12 b 10 d B 89 a 6 c 14 A 23 15 68 B

17 Find an angle in which the sin x is the same as the tan a b C 2 t d RIN 117

4 Given the point 4 3 find the cos x a b 3 5 3 c 2 14 d 415 4 3

12 The value of sin a b 4 3 l al C d 3 2

of the function f x e x 0 we have So 0 where a sin ka 1 q k 9 da

The Tubular Ride Boogie Board Company has manufacturing plants in Tucson Arizona and Toronto Ontario and you have been given the job of coordinating distribution of their latest model the Gladiator to their outlets in Honolulu and Venice Beach The Tucson plant can manufacture up to 640 boards per week while the Toronto plant beset by labor disputes can produce no more than 410 Gladiator boards per week The outlet in Honolulu orders 500 Gladiator boards per week while the Venice Beach outlet orders 550 boards per week Transportation costs are as follows Tucson to Honolulu 10 per board Tucson to Venice Beach 5 per board Toronto to Honolulu 20 per board Toronto to Venice Beach 10 per board Your manager has said that you are to be sure to fill all orders and ship the boogie boards at a minimum total transportation cost How will you do it Tucson to Honolulu Tucson to Venice Beach Toronto to Honolulu Toronto to Venice Beach boards per week boards per week boards per week boards per week

Find the exact value of each angle given sin 75 O al a 1 3 2 2 b 1 3 2 2 O c 1 3 2 d 1 3 2

The x value s for the function f x 2x tan x on the interval x where the slope of the function is zero is are a TC d 4 O c I 4 and Ob and 2 JC 4 FIN 2

Find the first term a1 and the common difference d of the arithmetic sequence 25 8 13 18 23 B a1 8 d 5 C a 8 d 8 A a1 5 d 13 D a1 5 d 3 25

where t is the time since it was removed from the oven measured in minutes cake in degrees Fahrenheit after it is removed from the oven is C t 70 110e kt 5 Determine the temperature of the cake when it was pulled out of the oven Use mathematics to justify your answer CCD 70 110 e kt Ccos 70thlee Crocho jut 14 0 70 1loc 70 110x1 6 If the cake is 160 F at t 3 minutes determine the value of the constant k Give your answer correct to three decimal places 70 1102 3 k ects 160 and 3 160 70 110 e the 110x 160 70 90 Ne xin 12 0 067 7 Determine the perfect time to the nearest minute to eat the cake if the perfect temperature for eating the cake is 99 F Use mathematics to justify your answer 3

Attempt to solve on a semi infinite interval 0 00 using the sine transform du J u t 0 2 u 0 t Aet u x 0 0 120 k lim f x 0

The figure to the right shows a transformation 1 of y X a Find a possible formula for the graph 1 x 15 X y Y 7 x 27 X 4 The x intercept is The y intercept is N 7 0 0 4 10 Y 9 8 b Write the formula from part a as a ratio of two linear polynomials X 0 r 7 6 5 4 c Find the coordinates of the intercepts of the graph NOTE Enter the exact answers 3 2 2 6 8

Determine the order of the following matrix J 6 3 9

What is the y intercept of the polynomial f x defined below Write the y value only f x 5x x

Which type of conic section does the following equation represent x 9 36 O hyperbola O not a conic section y 5 25 circle O ellipse 1 Submit Answer

The graph of y f x is the solid black graph below Which function represents the dotted graph 10 9 8 7 6 5 Oy f x 1 2 Oy f x 1 2 4 73 2 1 10 9 8 7 6 y 2 173 14 5 D 8 10 1 2 3 4 5 6 7 8 Oy f x 1 2 Oy f x 1 2 9 10 Submit Answer

In Exercises 41 and 42 find a3 a4 and a5 an 1 1 an 1 an 2 41 a 1 a 3 an 1 a 3 a

Determine the radius and interval of convergence of the given power series 2x 1 2n Inn 16 n 2

25 x y 2z 4 2x 3y 3z 5 3x 3y 7z 14

ind lim cos 1 x 1 1 n

If tan a 21 0 x 90 then find the exact value of each of the following 20 a sin a sin b cos na 2 c tan Simplify your answer including any radicals Use integers or fractions for any numbers in the expression Rationaliz the denominator

Determine whether the positive or negative sign results in a true statement sin 125 t sin 125 1 cos 250 2 1 cos 250 2

Fill in the blank so that the resulting statement is true sec B sec 1 1 cos 20 2 2 1 cos 20 1 cos 20 2 2

3 Identify the amplitude and period for the equation y 4sin3x 2 2 T a a 4 pd 3 b a 4 pd 3 d a 2 pd 4 c a 2 pd 3

log 2 x x sin x 1 x Check the continuity of the function f x lim 71 900 A Conitinuous at x 1 B Continuous at x 0 C Discontinuous at x 1 at x 0 D Discontinuous

A superintendent has 12 schools under his jurisdiction If he randomly selects schools from these 12 how many different combinations are possible

End the domain of the rational function x 3 14 g x X 2 A 2 u 2 0 C B 0 U D 3 u

3 1 1 1 49 Find the value of r for this series 4 4 12 36 108 A B 3 114 C 3 3 D www

x 2y 0 45 Solve the system 4y 3x 0 What is one solution A B 0 0 C 2 0

25 Use the Binomial Theorem to expand the expression 2 1 A y10 5y8 10y 10y4 5y 1 B y10 5y8 20y 20y4 5y 1 C y10 5y8 10y6 10y4 5y 1 D y10 5y8 20y6 20y4 5y 1

21 The perimeter of a triangle is 26 inches If the longest side is twice as long as the shortest side and the third side is 2 inches longer than the shortest side Which algebraic equation would best represent the side lengths of the triangle A x 2y z 2 26 B x x 2 2x 26 C x 2y 2z 26 D x 2x 3x 26

5 X y 2z 7 Use the elimination method to find the solution for x 2x y z 5 3x 2y z 6 A 0 B no solution C infinite solutions

16 If you have 8 friends and 4 gifts to give in how many ways can you give the gifts to friends if the gifts are all the same 81 A C 8 4 4141 1680 81 B C 8 4 4141 70 81 C P 8 4 41 1680 81 D P 8 4 41 70

1 Use the Binomial Theorem to find the coefficient of the fifth term 2x 1 7 A C 7 4 B C 7 5 C C 7 3 D C 6 5

Question 11 of 20 1 point Below is the graph of a polynomial function with real coefficients All local extrema of the funct 8 6 104 8 16 stion 10 Negative 6 10 Use the graph to answer the following questions a Over which intervals is the function decreasing Choose all that apply 7 7 2 2 4 4 8 2 8 8 00 b At which x values does the function have local minima If there is more than one value separate them with commas 7 4 c What is the sign of the function s leading coefficient d Which of the following is a possibility for the degree of the function Choose all that apply

Solve the following equation completely 62 3 88 2042 144 01 with multiplicity with multiplicity and with multiplicit

Find the number b so that the function f x is continuous everywhere 5x3 5 There is no such value for b Ob 6 b 6 bx cos x x 1 3x 9 Ob 12

28x 5 SHORT ANSWER Write the word or phrase that best completes each statement or answers the question Show that f and g are inverses of each other by verifying that f g x x g f x 3 f x x g x x 3

Evaluate the expression 1 8 f 8 when f x A 84 and g x 3x 3 B 24 c 25 D 9

Find an equation of the line tangent to the graph of f x 15 x equation in the form y mx b What is your value for b Write your exact numerical answer in the box below at the point where x 8 Write your

Evaluate the limit lim 1 0 4 4 cos x x x Enter your exact numerical answer in the box below

Let G x tan5 x Use the chain rule to determine G x Which of the following best describes your use of the chain rule O The inside function is y 25 and the outside function is y tan z O The inside function is y sec x and the outside function is y x5 O The inside function is y O The chain rule must be used at least two times tan x and the outside function is y 25 T

The function f is defined and continuous for all real numbers and its values are always less than 5 Determine the following limit lim 10x There is not enough information to determine the limit O O

Use an algebraic technique to evaluate the limit below Which technique did you use and what limit did you find lim 2 1 2x 3x x 8x 9 Q Using direct substitution the limit does not exist O Using multiply by the conjugate the limit is 2 5 O Using factor and cancel the limit is 0 O Using factor and cancel the limit is 2 5

The graph of y f x is shown below Use the graph to estimate the limit lim f x 24 8 10 8 6 4 2 44 6 5 4 3 0 1 2 3 4 5 6 7 2 4 6 8 10

12 Determine the convergence or divergence of the series and explain 52 2 Inn n b n 3 3 n 1 a n 2

art 1 Solve the 1 Find the convergence radius and interval of convergence of the Power Series n xn n 1 7n

The limit of the sequence in 146 ne 162 n 158n tan 91 n 00 n 1 is Hint Enter the limit as a logarithm of a number could be a fraction