# Limits & Continuity Questions and Answers

High School Calculus
Limits & Continuity
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
High School Calculus
Limits & Continuity
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
High School Calculus
Limits & Continuity
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
High School Calculus
Limits & Continuity
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
High School Calculus
Limits & Continuity
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
High School Calculus
Limits & Continuity
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
High School Calculus
Limits & Continuity
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
High School Calculus
Limits & Continuity
8 Solve the triangle by finding all missing side lengths and angle measures Round to the nearest tenth 5 39 R 94
High School Calculus
Limits & Continuity
The graph of y Tanx is shown Write the coordinates of point A as an ordered pair y arctan x m 2
High School Calculus
Limits & Continuity
Simplify the expression 1 sin cot
High School Calculus
Limits & Continuity
7 The graph of the derivative off is shown in the figure bellow W of f A C D E
High School Calculus
Limits & Continuity
x x 3x 4 X 2
High School Calculus
Limits & Continuity
3 Find the dimensions of a rectangle of area 324 ft that has the smallest possible perimeter
High School Calculus
Limits & Continuity
C cos OS 1 cos 777 COS 6
High School Calculus
Limits & Continuity
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
High School Calculus
Limits & Continuity
11 log 3x log 10 log 6 63
High School Calculus
Limits & Continuity
3 Inx In7 In63
High School Calculus
Limits & Continuity
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
High School Calculus
Limits & Continuity
Determine the end behavior of 2 f x 5x x 4 x 2 5 x 3
High School Calculus
Limits & Continuity
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
High School Calculus
Limits & Continuity
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
High School Calculus
Limits & Continuity
4 y cot 20 2 A B D 3x 2x 3x 7 270 4 2 Period Period Period x Period I
High School Calculus
Limits & Continuity
5 y cot 6 A B D 2 45 6 A 3r 8 2 3x 2r
High School Calculus
Limits & Continuity
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
High School Calculus
Limits & Continuity
A tangent function of the form y tan be has no vertical asymptotes for 2 x 2 Find a possible value of b
High School Calculus
Limits & Continuity
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
High School Calculus
Limits & Continuity
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
High School Calculus
Limits & Continuity
4 3 2 1 3 2 Y 2 3 You might need 2 What is the slope of the line 3 Lato
High School Calculus
Limits & Continuity
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
High School Calculus
Limits & Continuity
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
High School Calculus
Limits & Continuity
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
High School Calculus
Limits & Continuity
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
High School Calculus
Limits & Continuity
2 Write an equation of a cosecant curve with asymptotes at x
High School Calculus
Limits & Continuity
7 f x 3x 6x 1x 1 ax 3 x 1
High School Calculus
Limits & Continuity
6 f x Sax4 x 4 x 2 bx 5 x 2
High School Calculus
Limits & Continuity
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
High School Calculus
Limits & Continuity
f x x 3x 22 4x 10 3x 22 x 3 x 3
High School Calculus
Limits & Continuity
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
High School Calculus
Limits & Continuity
3 Graph y sin x 1 T TT 2 3 2 1 0 1 TT 2 TT 3TT 2 2TT x
High School Calculus
Limits & Continuity
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
High School Calculus
Limits & Continuity
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
High School Calculus
Limits & Continuity
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
High School Calculus
Limits & Continuity
Perform the subtraction and write the result in standard form Simplify your answer completely 123i 4 7i
High School Calculus
Limits & Continuity
Using the equation below describe the transformations from the parent function s x x 7 8
1