Limits & Continuity Questions and Answers

Sketch the graph of the y 2 cos x 1 2 37 k k K12 2 k12 3 3 2x 2 3 KIN KIN KIN 2 k KIN 13 X 2 k2 KIN k

Two planes leave the Atlanta airport at the same time and fly for three hours Flight 1504 flies 34 West of North at 245 miles per hour and Flight 168 flies 70 East of North at 271 miles per hour After 3 hours how far apart are the planes Round to the nearest hundredth 34 N 70

The function is given by j x 4 3 tan A x 1 2zk where k is an integer B x k where k is an integer 22 C x zk where k is an integer D x x 2xk where k is an integer Which of the following gives the vertical asymptotes of j

2 In AABC mZB 57 and AB 10 Which measure of segment AC would cause there to be two possible ways to draw the triangle A 6 B 9 C 12 D 15

Use a calculator to evaluate the trigonometric function Round your answer to four decimal places Be sure the calculator is se the correct angle mode cot 117

Use the angle conversion capabilities of a graphing utility to convert the angle measure to decimal degree form Round your answer to three decimal places if necessary 116 45

4 Which of the following statements is FALSE A sin S sin O x Y z X B sin H sin O C z sin O y sin H D X sin S 2 sin H 2 S X Y H

8 Solve the triangle by finding all missing side lengths and angle measures Round to the nearest tenth 5 39 R 94

The graph of y Tanx is shown Write the coordinates of point A as an ordered pair y arctan x m 2

Simplify the expression 1 sin cot

7 The graph of the derivative off is shown in the figure bellow W of f A C D E

x x 3x 4 X 2

3 Find the dimensions of a rectangle of area 324 ft that has the smallest possible perimeter

C cos OS 1 cos 777 COS 6

The graph below is the function f x 5 4 3 2 1 5 43 2 1 1 2 3 5 x 2 1 2 3 4 5 Select all statements below that you agree with Note You may be checking more than one box No partial credit f 2 is defined lim f x exists f x f 2 lim x 2 The function is continuous at x 2 The function is not continuous at x 2

11 log 3x log 10 log 6 63

3 Inx In7 In63

2 If sin 0 788 and cos 0 0 616 find each of the following Round to the nearest thousandth a sec 0 b cot 0 C csc 0 d tan

Determine the end behavior of 2 f x 5x x 4 x 2 5 x 3

Solve the logarithmic equation algebraically Approximate the result to three decimal places If there is no solution enter NO SOLUTION X 16 In x 8

Use a calculator to evaluate the function at the indicated value of x Round your result to the nearest thousandth f x 6 3e x X 100 X 2 344

4 y cot 20 2 A B D 3x 2x 3x 7 270 4 2 Period Period Period x Period I

5 y cot 6 A B D 2 45 6 A 3r 8 2 3x 2r

11 People are entering a museum at a rate modeled by f t people per hour and exiting the buildin at a rate modeled by g t people per hour where t is measured in hours The functions f and g are honnegative and differentiable for all times t Which of the following inequalities indicated that the ate of change of the number of people in the building is decreasing at time t a g t 0 b g t 0 c f t g t 0 d f t g t 0

A tangent function of the form y tan be has no vertical asymptotes for 2 x 2 Find a possible value of b

Find the average rate of change of f x of f x sin x In x on the interval 1 x a Sin 1 In 1 Sinaing 1 9

15 What are all values of x for which the function f defined by f x x 32 9x 7 is increasing A x 3 or x 1 B x 1 or x 3 C 3 x 1 D 1 x 1

4 3 2 1 3 2 Y 2 3 You might need 2 What is the slope of the line 3 Lato

Consider the function f x 9x Graph the exponential function by hand 2 2 Identify any asymptotes 1 1 150 100 50 y 150 100 50 1 2 2 3 X 4 1 3 2 2 3 1 4 5 1 x X

2 A math tutor makes 15 00 per hour in the tutoring lab at her school She earns an additional 7 50 more per hour overtime for any hours worked which exceed her normal 40 hr work week a Which graph depicts her toal salary for the week as a function of number of hours worked 4 points 1200 posi

3 Determine the following about the graph of the equation 8 6 a b y 3 X X Is the graph symmetric with respect to 1 The X axis 2 The Y axis 3 The origin Identify all asymptotes of the graph

4 Consider the graphs of f x sin 2x and g x csc 2x a Describe the transformations of the graphs of y sinx and y cscx that produce the graphs of f and g b List the four x intercepts of the graph of f c List four vertical asymptotes of the graph of g

2 Write an equation of a cosecant curve with asymptotes at x

7 f x 3x 6x 1x 1 ax 3 x 1

6 f x Sax4 x 4 x 2 bx 5 x 2

3 Determine if the functions are differentiable at the given x value prove continuity first and then prove differentiability If needed f x co 2x x 10 x 5 50 14x x 5 5x 2x 1 x 3

f x x 3x 22 4x 10 3x 22 x 3 x 3

8 Given f x 6 11 find all c in the interval 2 5 such that f c f 5 2 5 2 A 15 C 15 B 10 D 10

3 Graph y sin x 1 T TT 2 3 2 1 0 1 TT 2 TT 3TT 2 2TT x

Find the instantaneous rate of change of th function at the given x value Use the form f a h f a lim h 0 h 2 f x 4x 1 at x 2

Kai says the amplitude of y cos x is 2 since the distance between the maximum and the minimum value is 2 Is Kai correct Explain

Consider the following function f x 3x 8x 4 2x 3x 2 Find all vertical asymptotes horizontal asymptotes slant asymptotes and holes in the graph of the function Then use a graphing utility to verify your result Enter your answers as comma separated lists If an answer does not exist enter DNE vertical asymptote horizontal asymptote slant asymptote hole x y y x y

Perform the subtraction and write the result in standard form Simplify your answer completely 123i 4 7i

Using the equation below describe the transformations from the parent function s x x 7 8