Limits & Continuity Questions and Answers

A football player punts a ball at an angle of 45° at 1.5 feet off the ground, with an initial velocity of 78 feet per second. How far away does the ball land, in feet, when hitting the ground?

Given sinθ = 8/17 and cosθ = 15/17 which of the following can be proven using a Pythagorean identity? 1 + (8/17)^2 = (15/17)^2 1 + (15/17)^2 = (8/17)^2 (8/17)^2 + (15/17)^2 = 1 (8/17)^2 - (15/17)^2 = 1

1 Which of the following is the simplified expression of 1+ 1/cotθ tanθ?

The concentration, C, of phenylbutazone, in micrograms per milliliter (µg/mL), in the plasma of a calf injected with this anti-inflammatory agent is given approximately by C(t) = 42.06 e^ -0.01042t, where t is the number of hours after the injection and 0 st≤90. a) Given that the model is accurate for 0 st≤ 90, what is the initial dosage? b) What is the average amount of phenylbutazone in the calf's body for the time between 15 and 90 hours?

Given y=√x. Find dx/dt when y=7 and dy/dt = 1.55.

Assume that x = x(t) and y=y(t). Let y = x² +2 and dx/dt = 4 Find dy/dt when x = 3.

Let x = -16π/3 Part A: Determine the reference angle of x.

f(x) = 3x+12/x-4 Finds a. relative maximum and minimum b. vertical and horisontal asymptotes c. Graph

Use the two given functions to write y as a function of x. y = 4a-1, a = - 4x +3 y = (Simplify your answer.)

Graph the solution to the following inequality on the number line. (x+6) (x+1)>0

Let f(x) = x/2 - sin πx/6. Find all values of c in the interval (-1, 0) such that f'(c) =

The count in a bacteria culture was 800 after 20 minutes and 1200 after 30 minutes. Assuming the count grows exponentially, What was the initial size of the culture? Find the doubling period. Find the population after 80 minutes. When will the population reach 11000.

Solve the equation |5x + 2| = 14 The solutions are:

Let f(x) = 1/x-6 and g(x) = 7/x + 6 Find the following functions. Simplify your answers. f(g(x)) = g(f(x)) =

Consider f(y) = -13y - 26 sin(y) on [0, 2π]. Determine the intervals on which f is decreasing. f is decreasing on: f is decreasing nowhere. Determine the intervals on which f is increasing. f is increasing on: f is increasing nowhere. Determine the value and location of any local minimum of f. Enter the solution in (y, f(y)) form. If multiple solutions exist, use a comma-separated list to enter the solutions. f has a local minimum at: f has no local minimum. Determine the value and location of any local maximum of f. Enter the solution in (y, f(y)) form. If multiple solutions exist, use a comma-separated list to enter the solutions. f has a local maximum at: f has no local maximum.

Finding x- and y-intercepts given a polynomial function Find all ercepts and y-intercepts of the graph of the function. f(x) = 3x² +5x-12 If there is more than one answer, separate them with commas. Click on "None" if applicable.

Find a polynomial f (x) of degree 4 with real coefficients and the following zeros. 1 (multiplicity 2), -2+3i

Determining the end behavior of the graph of a polynomial... (a) f(x)= = -2x + 2x - 7x + 4 Falls to the left and rises to the right Rises to the left and falls to the right Rises to the left and rises to the right Falls to the left and falls to the right (b) f(x) = 2x3 + 9x2 - 6x-4 Falls to the left and rises to the right Rises to the left and falls to the right Rises to the left and rises to the right Falls to the left and falls to the right (c) f(x) = -5x (2x - 5)² Falls to the left and rises to the right Rises to the left and falls to the right Rises to the left and rises to the right Falls to the left and falls to the right

For the polynomial below, 2 is a zero. g(x)=x² =x² + 4x² Express g (x) as a product of linear factors. www. 10x - 4

Use this to find all zeros of the function. f(x) = 5x³+x²2-20x-4 If there is more than one zero, separate them with commas. Write exact values, not decimal approximations

For the polynomial below, -2 is a zero. f(x)=x² + 3x² - 4x - 12 Express f(x) as a product of linear factors.

Find a mla -4, 3, 2-i f(x) = 11 degree 4 with real coerricle and the following zeros 0² x 5 U

For the omial below, 2 and 1 are zeros. 4 3 f(x)=x²-x³-8x² +16x-8 Express f(x) as a product of linear factors. 2

f(x)=2x²+8x+7 Identify the transformations for the given parabolic function, click all that apply. Hide answer choices A shifts left 2 B) vertical shrink by 2 vertical stretch by 2 D) shifts up 1 E shifts right 2 (F) shifts left 1 G shifts down 1 (H) rotates downward around the x-axis rotates upward around the x-axis shifts up 2

Consider f(x) = -12 arcsin (625) Determine the intervals on which f is decreasing. Of is decreasing on: Of is decreasing nowhere. Determine the intervals on which f is increasing. Of is increasing on: Of is increasing nowhere. Determine the value and location of any local minimum of f. Enter the solution in (x, f(x)) form. If multiple solutions exist, use a comma-separated list to enter the solutions. of has a local minimum at: Of has no local minimum. Determine the value and location of any local maximum of f. Enter the solution in (x, f(x)) form. If multiple solutions exist, use a comma-separated list to enter the solutions. of has a local maximum at: Of has no local maximum.

Question 6 of 10 (1 point) | Attempt 1 of Unlimited View question in a popup Car inspection: Of all the registered automobiles in a city, 11% fail the emissions test. Fourteen automobiles are selected at random to undergo an emissions test. Round the answers to at least four decimal places.

(a) Find the largest number 6 such that if Ix - 3| < 6, then [5x - 15| < &, where & = 0.5. d≤ (b) Repeat part (a) and determine & with & = 0.05. d≤

Find a function that has derivative f'(x) = -6x-6 and with graph passing through the point (-6, 1).

Locate the absolute extrema of the function g(x)= 3x +5 on the closed interval [0, 5]

Determine the value of k 5, f(x) = {kx + 5₁ A k=4 B. k=1 C. k=2 D. k= 5 IN 2 for which f(x) is continuous. x <3 (x² + k, x ≥ 3 K

Find the length and width (in feet) of a rectangle that has the given area and a minimum perimeter. Area: 25 square feet ft (smaller value) ft (larger value)

Find c> 0 such that the area of the region enclosed by the parabolas y = x² - c² and y = c² - x² is 190. C =

Use - ∞o or ∞o where appropriate to describe the behavior at each zero of the denominator and identify all vertical asymptotes. f(x) = 2x/x+8 Identify all vertical asymptotes. Select the correct choice below and, if necessary, fill in the answer box(es) to complete your choice. A. From left to right the asymptotes are___,____and____ (Type equations.) B. From left to right the asymptotes are___and_____ (Type equations.) C. The asymptote is____ (Type an equation.) D. The function has no vertical asymptotes.

Use - ∞ or ∞ where appropriate to describe the behavior at each zero of the denominator and identify all vertical asymptotes. f(x) = 2x/x+8 Locate all zeros of the denominator and describe the behavior of the function at those values. Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice. As x approaches the smaller zero from the left and right, f(x) approaches and respectively. As x approaches the A. There are two zeros. The smaller zero is x= and the larger zero is x = larger zero from the left and right, f(x) approaches and respectively. B. There is one zero, at x = As x approaches this zero from the left and right, f(x) approaches and respectively. C. There are no zeros of the denominator.

Find the limit if it exists. lim 4x X→8 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. lim 4x = X→8 (Simplify your answer.) B. The limit does not exist.

Find lim f(6 +h)-f(6)/h if f(x) = 4x - 1. h→0 lim f(6 +h)-f(6)/h if f(x) = 4x - 1. h→0 (Simplify your answer.)

Find the limits in a) through c) below for the function f(x) =x²-9x+8/ x+8 Use ∞ and ∞ when appropriate. a) Select the correct choice below and fill in any answer boxes in your choice. A. lim f(x)= X--8- B. The limit does not exist and is neither - ∞ nor ∞.

For the given function f, evaluate f(-4), ƒ (-3), ƒ (-2), and f(-1). f(x) = 2 if x≤-4 -4 if x>-4

For the given function f. evaluate f(-3), f(-2). f(-1), and f (0). f(x) =-2x²+3 if x < -1 4x-2 if x>-1 f(-3) = f(-2)= f(-1) = f(0) =

Find (A) the leading term of the polynomial, (B) the limit as x approaches ∞o, and (C) the limit as x approaches - ∞ p(x) = 5x + x² - 6x6 (A) The leading term is (B) The limit of p(x) as x approaches ∞ is (C) The limit of p(x) as x approaches-∞ is

What is the area of the sector of a circle who's radius is 43.5 cm and is bounded by an arc of π/12 radians? A. 247.7 cm2 B. 5.69 cm² C. 946.13 cm² D. 495.39 cm²

The position of an object is given by s(t) = In(t³). What is the displacement of the object between t = 1 and t = 4? A. 3 B. 4.159 C. 4.328 D. 16.87

Find each function value and limit. Use - ∞o or co where appropriate. f(x) = 3x² - 6x² / 10x⁵ + 5 (A) f(-6) (B) f(-12) (C) lim f(x) (A) f(-6)= (Round the nearest thousandth as needed.) (B) f(- 12) = (Round to the nearest thousandth as needed.) (C) Select the correct choice below and, if necessary, fill in the answer box to complete your choice.

Let f(y) = -4-3y² + 8y Determine the critical values of f. If multiple such values exist, enter the solutions using a comma-separated list.

For the polynomial below, -3 is a zero. h(x)=x³ + 9x² + 25x + 21 Express h (x) as a product of linear factors.

Use the Factor Theorem to determine whether x + 3 is a factor of P(x) = x³ + 2x² +7. Specifically, evaluate P at the proper value, and then determine whether x + 3 is a factor.

For f(x) = 1/6+x², the slope of the graph of y = f(x) is known to be -2/49 at the point with x-coordinate 1. Find the equation of the tangent line at that point.

Use the Factor Theorem to determine whether x +2 is a factor of P(x) = -2x⁴-2x³+4x+24. Specifically, evaluate P at the proper value, and then determine whether x + 2 is a factor.

For the polynomial below, 2 is a zero. g(x)=x³ - 8x² + 16x - 8 Express g (x) as a product of linear factors.

Find all asymptotes (vertical, horizontal, and/or slant) for y = x³ / (x²-16 )