Limits & Continuity Questions and Answers

Find the limit, if it exists. (If an answer does not exist, enter DNE.) lim x-6 / x² + 3 x→-∝

Use the remainder theorem to find P (3) for P(x) = -2x³ +6x²-x-5. Specifically, give the quotient and the remainder for the associated division and the value of P (3).

(-4x³+9x²-20x4+5-8x) ÷ (-4x²+1) Write your answer in the following form: Quotient +

Use the remainder theorem to find P (1) for P(x)=x+-4x³-4x² +9. Specifically, give the quotient and the remainder for the associated division and the value of P (1).

A boat travels 26 miles east from a lighthouse then changes direction traveling 15° south of west for 13 miles. How far is the ship from the lighthouse? [?] miles

For the polynomial below, 1 is a zero. f(x)=x² + 4x² + x - 6 Express f(x) as a product of linear factors.

For the polynomial below, 2 is a zero. h(x)=x³ - 8x² + 14x - 4 Express h (x) as a product of linear factors.

Divide. (-3-14x+10x³): (5x²-4) Write your answer in the following form: Quotient +

Find the domain of the function. f(x) = √(3-8x)

Consider h(y) = - 5y²-8y - 9 on [ - 4, 2]. Determine the interval over which h is continuous and the interval over which h is differentiable. h is continuous on h is differentiable on

Consider h(x) = x² + 10x + 23 on [-7, -5]. Determine the interval over which h is continuous and the interval over which h is differentiable. h is continuous on h is differentiable on

Consider g(x) = − 4x log9( – 6x) on [ –3/2,-1/6] Determine the interval over which g is continuous and the interval over which g is differentiable. g is continuous on g is differentiable on

Consider g(x)=-2x² +5 on [1,1]. Determine the interval over which g is continuous and the interval over which g is differentiable. g is continuous on g is differentiable on

Consider h(t) = t^3 + 3t² - 9t-3 on [-5, -2]. Determine the interval over which h is continuous and the interval over which h is differentiable. h is continuous on h is differentiable on

Consider f(t) = 4e^¯t on [-6, 1]. Determine the interval over which f is continuous and the interval over which f is differentiable. f is continuous on_________ f is differentiable on_________

Consider h(y) = ln (11y - y² - 27) on [4, 7]. Determine the interval over which h is continuous and the interval over which h is differentiable. h is continuous on________ h is differentiable on________

Determine the interval over which g is continuous and the interval over which g is differentiable. Consider g(w) =w² - 3w - 54/(w + 7)on [ - 6, 9]. g is continuous on________ g is differentiable on_________

Which of the following has a slant asymptote when graphed? y =6/(x+2) y=4x/(x+2) y =2x²+3 /(x+2) y=3x³-1/( x+2)

A bus travels 8.4 miles east and then 14.7 miles north. What is the angle of the bus' resultant vector?

For the function, find f(2), f(3), and f(-1). f(x) = 2x² - x f(2) = 6 f(3) = 16 f(-1) = 0

Write an expression to match the statement below. Add 5 to 48 divided by 12.

Middle C has a frequency of 264 cycles. Which of the following has the same frequency as middle C? t = time in seconds Enter a, b, c, or d. 1050 t) a. y = 8 sin (1050T b. y = 7 sin(530ft) 3 c. y = 9 sin(1600 0T t) d. y = 8 sin(1584 t) 3

Find the horizontal asymptote(s) of f(t)= (A) y = 9 (B) y = 6 9 4 (C) y = (D) y=-6 (E) There are no horizontal asymptotes. 27t-18 3t+8

Find the value of m for which h(x) = continuous function. (A) 7-√37 (B) -3 (C) 3 (D) 7 (E) 7+√37 5x-13, x<2 x²-7x+m, x>2 is a

Find the vertical asymptote(s) of f(x)= (A) x = 1 (B) x=-1 (C) x = 1 and x = -1 (D) y = 1 (E) y=-1 x²+2x+1 2 x²-1

For what value of h is f(x)= 5₂ x ==? 2 (A) -3 (B) 0 (C) 3 (D) (E) 25 2 19 2 6x²-11x-10 2x-5 h, x= 4 5/2 5 2 continuous at

Is 275° coterminal with-1525°? Yes No

How would you limit the domain to make this function one to one? f(x)=x²-5 Your answer will be the point to which you would limit the function. So if you would restrict the domain to either all x values greater than or equal to two or all x values less than or equal to two, you would simply enter 2.

The figure to the right shows the number of full-time employees of a company (in millions) as a function of the revenue generated by the company (in billions). Find and interpret the average rate of change of employees with respect to revenue for the following changes in revenue. (a) $5 billion to $31 billion (b) $31 billion to $107 billion (c) $5 billion to $107 billion CO (a) The average rate of change of employees with respect to revenue for the changes from $5 billion to $31 billion is about employees/billion dollars. (Round to the nearest thousands as needed.) Employees (millions) AY 70- 60- 50- 40- 30- 20- 10-15.11 (107.55 3131 0 20 40 60 80 100 120 Revenue (billions)

Find the area of this triangle if C = 12 radians, a = √57, and b = 8.9. A B a [?] square units Round to the nearest tenth.

For the polynomial below, 2 is a zero. 3 f(x)=x²³ - 4x² + 2x + 4 Express f(x) as a product of linear factors. f(x) = 0

Consider the following quadratic function. g(x) = -2x² + 4x +3 (a) Write the equation in the form g(x) = a (x-h)² + k. Then give the vertex of its graph.

f(x) = 2x² - 20x +49 Does the function have a minimum or maximum value? Minimum O Maximum What is the function's minimum or maximum value? Where does the minimum or maximum value occur?

Find an equation of the plane. the plane through the points (0, 2, 2), (2, 0, 2), and (2, 2, 0)

Consider the following relation. x = -5|y| +5 Step 1 of 2: Find four points contained in the inverse. Express your values as an integer or simplified fraction.