Limits & Continuity Questions and Answers

Consider the given function m x x 2 1 a Determine whether the graph of the parabola opens upward or downward b Identify the vertex c Determine the x intercept s d Determine the y intercept s e Sketch the function f Determine the axis of symmetry g Determine the minimum or maximum value of the function h Write the domain and range in interval notation Write your answers in exact form Part 1 of 9 a Determine whether the graph of the parabola opens upward or downward The graph of the parabola opens downward Part 1 9 Part 2 of 9 b Identify the vertex

Suppose that the manufacturer of a gas cloth

Problem 2 Linearize the following equations and show all steps as needed a y bemx b y c cos y x ax b d y x e xa 1 x ax x d

K A 25 ft ladder is leaning against a house when its base starts to slide away By the time the base is 24 ft from the house the base is moving away at the rate of 14 tu sec a What is the rate of change of the height of the top of the ladder b At what rate is the area of the triangle formed by the ladder wall and ground changing then c At what rate is the angle between the ladder and the ground changing then a The rate of change of the height of the top of the ladder is Simplify your answer b The area is changing at Simplify your answer c The angle is changing at Simplify your answer ft sec rad sec fu sec

find the limit b lim In x X18 x3

stion list K Determine whether th does represent a fund

Use the four step process to find the slope of the tangent line to the graph of the given function at any point Simplify f x 4x 9x Step 1 Step 2 Step 3 Step 4 f x lim h 0 f x h f x h f x f x h f x h f x h f x h

Michelle invests 39 900 in a partnership that has four other partners The total investment of all partners is 240 000 What percent of the business does Michelle own Round to the nearest whole percent if needed

The equation of the unit circle is x y 1 O True O False

Analyze the graph of the function x 10 x x 17 R x a What is the domain of R x A xx 0 and x 17 B x x 0 and x 17 and x 10

Find the value of the limit lim 2 4 5 ILU 9

Given that f x x 0h x h 1 3 h 1 6 Calculate f 1 Hint Use the product rule and the power rule uonti G

Gemma is creating a histogram based on the table below Number of People Salary Range 0 19 999 40 20 000 39 999 30 40 000 59 999 35 Which scale can she use for the vertical axis such that the difference in the heights of the bars is maxi O 0 50 O 0 40 10 50 25 40

x y 4 4 y 2 2 on the left and x y 2 2 on the right Find the volume of the solid obtai volving the region around each of the following a the x axis

22 Use the Squeeze Theorem to prove that begin array c lim x rightarrow infty frac tan 1 x x 0 g x left begin array cc x 2 text if x leq 1 2 x 2 text if x 1 end array right end array

Write out the first five terms of the sequence determine whether the sequence converges and if so find its limit a n 1 n 2

K Find the limit lim cos x 2 7x 3x X 2 lim cos x 2 7x7 X 3x 37 2 Simplify your answer

11 Find the derivative of the provided function using the LIMIT DEFINITION did it correctly by using differentiation rules to find it as well and then check that you f x

In the problem P x y is the point on the unit circle that corresponds to the real number t Find the exact value of the indicated trigonometric function of t 39 5 8 8 O A OB O C O D 39 8 Find csct 8 39 39 39 8 39

Find the reference angle for the angle 95

Find the exact value of the quadrantal angle csc 1260 C Select the correct choice below and if necessary fill in the answer box to complete your choice OA csc 1260 OB The value is undefined

F4U nomial Functions Slide 2 4 A bounce

Simplify the following and express the answer using no negative exponents a 2 x 7 3 b x y x 0y 1

Evaluate the expression rounding your answer to four significant digits where necessar 17 2 2 98

13 14 Explain in terms of linear approximations why the is reasonable approximation 13 In 1 05 0 05 14 1 01 1 06

A quadratic function f is given f x x 4x 5 a Express fin standard form f x x 2 1 b Find the vertex and x and y intercepts of f If an answer does not exist enter DNE vertex x y x intercept x y y intercept x y c Sketch a graph of f 10 9 8 7 6 5 to 10 TH 10 9 8 7 6 5 3 2 9 Fill Graph Layers After you add an obj can use Graph Laye properties

A quadratic function f is given f x x 4x 3 a Express fin standard form f x x 2 1 b Find the vertex and x and y intercepts of f If an answer does not exist enter DNE x y 2 1 vertex x intercepts x y y intercept x y v x y c Sketch a graph of f 10 9 8 7 10 10 4 09 2 1 10 9 8 7 6 5 4 3 2 N smaller x value larger x value Fill Graph Layers After you add ar can use Graph L properties

f if m is differentiable at 2 then f x is continuous at 2 TRUE FALSE

O O Use the equation y x 16 to answer parts a through g c Find the vertex The vertex of the parabola is 0 16 Type an ordered pair d Find the y intercept The y intercept is 0 16 Type an ordered pair e Find the x intercepts Select the correct choice below and if necessary fill in complete your choice OA The x intercept s is are ended

53 62 Circular Arcs Find the lengths of the circular arc the radius r of the circle or the central angle 0 as indicated 53 5 T 6 S 54 S 5 140

66 Sketch the graph of a continuous function f such that for f 1 2 4 5 1 0 x x 4 f has a relative maximum when x 4 and there is a vertical tangent line when x 4 X

1 O Use the equation a Determine whe O The parabola O The parabola

Draw the graph of the function and state the domain and ra f x 4x 1 Choose the correct graph below 4095 B Ay

Let A a b c d B a b c and C a d e f Choose the elements of the set A B nC Ob a

Equations and Functions Graph the function as a blue line or curve a the same set of axes as a red line or curve

IN O nd Inverse Expressions quations and Functions The following function is one to one Find the in graph the function and its inverse on the same f x 2x 1

Find the length s of the circular are s ro 5 140

ind the limit Use l Hospital s Rule where appropriate If there is a more elementary method consider using lim 4x In x X18

2 x 2 Graph the rational function f x 3 x 1Xx 1 O 5 4 3 2 2 32

Graph the solution set of the inequality where x is a rea

e the following inequality x 11x 0

Determine the quadratic function whose graph is given The vertex is 3 2 The y intercept is 0 7 f x Simplify your answer 5 10 15 Ay 10 O Q IN

e quadratic function f x 2x 2x 1 answer parts a th phing utility

Determine the x and y intercepts for the given function Write your answer as an ordered pair s x 4x 24 If there is more than one answer separate your answers with commas Select None if appropriate Part 1 of 2 x intercept s 0 0 0 0 None X

An invertible function f x is given along with a point that lies on its graph Using Theorem 2 7 7 evaluate f x at the indicated value 11 x 11e help numbers Point 0 11

Graph the solution set of the inequality where x is an in X

Question Part wn currently has 5000 resid where x 5000 1 208 0 3x ears and in 50 years

Graph the solution set of the inequality where xi

6 0 14 9 Is this set of ordered O No O Yes

1 O Fill in the blank The set of values that can be used The set of values that can be use