Limits & Continuity Questions and Answers

What are the quotient and remainder when 5x4 - 3x² is divided by x³ - x² y x²³ - x² +1? The quotient is and the remainder is.

Expand the following as sums and/or differences of simpler logarithmic expressions. In 3x√√x (2x+1)² 1 In 3x+-In x-21n (2x+1) 31n x+In √x-21n (2x+1) 1 In 3x+2lnx--In (2x+1) x-In (2x+1) 1 21n (2x+1)-In 3x+ - ln 3x+ ln x x

Select the statement(s) that are true about sampling distributions. 1. The shape of all sampling distributions are approximately normal. 2. The mean of the sampling distribution of a is equal to the mean of the distribution from which the sample was taken. 3. The standard deviation of the sampling distribution of a is equal to the standard deviation of the distribution from which the sample was taken divided by the sample size. 4. The shape of all sampling distributions are symmetrical. 01&3 2 only 3 only 0184 None of the above

19 sin (are sec (17)) = 19 an (arc sec (77)) = [ 7 19 X

A cell site is a site where electronic communications equipment is placed in a cellular network for the use of mobile phones. The numbers of cell sites from 1985 through 2008 can be modeled by y = 237,101 1+1950e-0.355t where t represents the year, with t=5 corresponding to 1985. Use the model to find the numbers of cell sites in the year 2007 O209,071 O 207,071 O 211,071 O 210,071 O 208,071

Let f(x) = 3x + 5 and g(x) = x². Perform each function operation. 2. g(x) = f(x) 1. f(x) + g(x) - 3. f(x) - g(x) 4. f(x) · g(x) 7. (f + g)(x) 10. (f- g)(x) . f(x) g(x) 8. (f- g)(x) 11. (g)(x) 5. 6. f(x) 9. (g - f)(x) 12. ()(x)

A cheesecake has equally sized slices. Each slice is a different flavor. The diameter of the cheesecake is 10 inches, and the area of the 25T slice of blueberry cheesecake is 12 square inches. How many slices does the cheesecake have? slices

A mass weighing 4 pounds is attached to a spring whose spring constant is 25 lb/ft. What is the period of simple harmonic motion? S

A population of bees are dying at the rate proportional to the size of the initial hive, H(t), where t is measured in days. If the hive has 500 bees June 1st, and only 450 bees 15 days later, how many bees will there be 30 days later? Round your answer to the nearest bee, and assume the growth is proportional to initial population. O 300 O 400 O 405 425

Analyze the polynomial function f(x) = 5x (x² − 9) (x + 4) using parts (a) through (e). (a) Determine the end behavior of the graph of the function. The graph of f behaves like y =___for large values of |x|.

Find a polynomial f (x) of degree 4 that has the following zeros. 5, 0, 7, -2 Leave your answer in factored form.

Divide. (8x²³ + 2x² +14x+24) ÷ (4x+5) Your answer should give the quotient and the remainder. Quotient: Remainder: 0 9 X 5 ?

www 0 a solution with a salt A very large tank initially contains 100L of pure water. Starting at time t concentration of 0.8kg/L is added at a rate of 5L/min. The solution is kept thoroughly mixed and is drained from the tank at a rate of 3L/min. Answer the following questions. 1. Let y(t) be the amount of salt (in kilograms) in the tank after t minutes. What differential equation does y satisfy? Use the variable y for y(t). Answer (in kilograms per minute): dy dt m 3y 100 + 2t 2. How much salt is in the tank after 40 minutes? Answer (in kilograms):

How many significant figures are in the measurement 16.400 g? 16.400 has

Calculate the volume of the cube and report the answer to the correct number of significant figures. 2.20 cm x 2.215 cm x 2.2 cm

Graph the parabola. 2 y=x² +6x+4 Plot five points on the parabola: the vertex, two points to the left of the vertex, and two points to the right of the vertex. Then click on the grap button.

A lighthouse is located 160 feet from the nearest point P on a straight shoreline. The revolving beacon in the lighthouse makes one revolution every 10 seconds. Find the rate at which a ray from the light moves along the shore at a point 115 feet from P.

Sketch a graph of f(x) Solution: - 3 X - 2x² - 3x 2 x² + 3x + 2 Before answering this question, we need to factor f(x). Factor f(x) completely and submit your answer below.

Determine the infinite limit. lim 10-x/ (x-9)² x→9 ∝ -∝

For the function f, how would you remove the discontinuity? In other words, how would you define /(2) In order for fto be continuous at 27 (2)=1 f(x) =

Let g(y) = arccos (√6y) Determine the derivative of g. g'(y) Determine the interval(s) on which g is differentiable. Report the solution using interval notation. = g is differentiable on

c(e-7t) Determine the derivative of h. Let h(t) = arcsec h'(t) =

Find x where 0≤x≤ 2. 4√2 tan x-√√2 = 3√2 tan > x π [?]' + T

Use Newton's method to approximate the indicated root of the equation correct to six decimal places. The positive root of 6 sin x = x² X =____

Let A(z) represent the area bounded by the graph, the horizontal axis, and the vertical lines at t= 0 and t = for the graph below. Evaluate A(z) for x = 1, 2, 3, and 4 5 M 2 4 3 A(1) = = A(2) - A(3) A(4) = = 3 4

Find lim h(x), if it exists. X→∞ f(x) = 4x² + 2x + 6 (a) h(x) = lim h(x) = X→∞ (b) h(x) = lim h(x) = X-8 (c) h(x) = = lim h(x) = X-8 f(x) X f(x) x² f(x) +3

Find x if π ≤ x ≤ 2π 2csc²x cos5x = √2cot²x cos²x X= [?] | JTC 2 4

Find the limit, if it exists. lim X-80 X+8 (x² + 5)¹/3

Find x where 0 ≤ x ≤ ³/1. 5√3 sin x = 3 + 3√√/3 sin x 77 7

Step 4 Step 2 To determine the critical numbers of g(x), set g'(x) equal to zero and solve for x. g'(x) = 0 g(x). g(x) = x² - 6x - 280 2(x-33) = 0 g'(0) = 9(x)=2x-6 g'(0) = 2(-3✔ Since g'(0) ✓ First consider the interval (-∞, 3). Let x = 0. g'(x) = 2(x-3) 9'(0) = 2(0✔ Step 3 Since there is no point for which g'(x) does not exist, x = 3 is the only critical number. Thus, the number line can be divided into two intervals (-∞, 3) and (3, ∞). Determine the sign of g'(x) at one test value in each of the two intervals. g'(4) = 2( g'(4) = 2( g'(4) = 2x-6=0 ✓ X= Step 5 Now consider the interval (3, ∞). Let x = 4. g'(x) = 2(x - 3) 2r-6 - 3) -3) - 3) 0, the function is decreasing ✔ webassign.net 205 decreasing in the interval (-∞, 3).

Does the relation represent y as a function of a? 2y +8 7y-3 No, because some values of a correspond to more than one value of y No, because the relation does not define y in terms of a Yes, because the relation is described by an equation containing and y Yes, because each value of a corresponds to exactly one value of y

Find each limit if it exists. 5x3/2 (a) (b) (c) lim. x-* 8x² lim X→ +5 5x3/2 8x3/2 + 5 5x3/2 lim x 8√x+5 →∞ 11 11

Does the relation represent y as a function of x? x= √√16-y6 No, because there are values of a that correspond to more than one value of y Yes, because the relation is described by an equation containing and y No, because the equation is not solved for y Yes, because each value of a corresponds to exactly one value of y

Does the relation represent a function? No, because there is an input value that corresponds to more than one output value Yes, because the input values are all different {(2,5), (6,2), (15,8), (8,5)} Yes, because the output values are all different No, because there is no pattern between the input and output values

Does the relation represent a function? No, because r appears as both an input value and an output value Yes, because the ordered pairs are distinct {(p, q), (r,s), (p,r)} No, because the input value p corresponds to two different output values Yes, because the output values are all different

Does the relation represent a function? X y OYes, because the input values are distinct OYes, because the output values are distinct 5 3 10 10 4 11 O No, because the input value 10 corresponds to two different output values Yes, because each input value corresponds to exactly one output value No, because there are distinct input values that correspond to the same output value

types of numbers that make up the set of real numbers: ● Natural numbers: 1, 2, 3, 4, ... • Integers: ,-3, -2,-1,0,1,2,3,... ● Rational numbers: ratios of integers. Examples: 2 *** 5 -- 23 0.23 = 100 Irrational numbers: real numbers that cannot be written as ratios of two integers Examples: √2, T 35: 35 - #6 Consider the set of numbers given in the set {0,-8, 25, 27, √5, 0.492, -, V2, 0.3= List the numbers that are a) Natural numbers: b) Integers: c) Rational numbers: d) Irrational numbers: e) Real numbers:

#7 Write an algebraic equation to represent the given information. Let x be the first number and y be the second number. a) the sum of the two numbers is 10 b) the first number is 2 more than the second number c) the first number is twice the second number d) The first number is 2 less than twice the second number e) The square of the first number is 2 times the second number. f) The total of the first number and ½ of the second number is 17.

Let f (t) be the number of ducks in a lake t years after 1990. a. What does the statement f (6) = 27 mean? There will be 27 ducks in the lake 6 years from now. In 27 years, there will be 6 ducks in the lake. In 1996, there were 27 ducks in the lake. In 1996, there were 27 more ducks than in 1990. b. What does the statement f (11) = 37 mean? O In the year 2001, there were 37 ducks in the lake. O In 37 years, there will be 11 ducks in the lake. Every 11 years, there are 37 more ducks in the lake. There will be 37 ducks in the lake 11 years from now.

#4: Find the slope and y-intercept of each line. Plot the y-intercept and use the slope to plot a second point. Then graph the line. a) y = 2x - 1 Y b) x+y=2 slope y-intercept: a second point: -4 -3 -2 -1 3 2 7 -2 -3 -4 2 3 X slope: y-intercept: a second point: -4 -3 -2 3 2 1 - -2 -3 1 2 3 X

An object oscillates as it moves along the x-axis. Its displacement varies with time according to the equation x = 3 cos (8mt + 1) where t is in seconds What is the frequency of this motion? [?] hertz

Simplify. sin x/1 + cos x +1 + cos x sin x ___

Solve the equation using U-substitution and enter the solution set below. Separate the solutions by a comma. Arrange the solutions in order from smallest to largest. Do not insert any blank spaces in your answer. For fractional answers, use the /symbol, e.g. 3/2. (2x + 5)² - 7(2x + 5) - 30 = 0

Evaluate the function at the indicated value. f(x=2x - 1/ 5x+4

How many significant figures are in the number 24.32? 24.32 has [?] significant figures.

Solve the equation. Enter your answer in solution set notation listing the solutions in order from smallest to largest separated by a comma. Do not include any blank spaces in your answer. (Example: (-1,5,8)) x³5x² - 4x + 20 = 0

The equation describes a 3x2-y+z2 (A) elliptic paraboloid (B) ellipse (C) one-sheeted hyperboloid (D) hyperbolic paraboloid (E) two-sheeted hyperboloid

What expression is needed to write the equation as a quadratic equation? x10x² +9=0 Select an answer and submit. For keyboard navigation, use the up/down arrow keys to select an answer. a u='x b u = x² c u = x² d u = x³

Which vocabulary word has the following origin?from Latin acadēmia A. persistent B. resilient C. eloquent D. academy

Find the horizontal shift. y = -1 cos(1/4-π/6)