# Limits & Continuity Questions and Answers

Calculus

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

Calculus

Limits & ContinuityUse 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).

Calculus

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

Calculus

Limits & ContinuityUse 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).

Calculus

Limits & ContinuityA 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

Calculus

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

Calculus

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

Calculus

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

Calculus

Limits & ContinuityConsider 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

Calculus

Limits & ContinuityConsider 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

Calculus

Limits & ContinuityConsider 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

Calculus

Limits & ContinuityConsider 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

Calculus

Limits & ContinuityConsider 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

Calculus

Limits & ContinuityConsider 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_________

Calculus

Limits & ContinuityConsider 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________

Calculus

Limits & ContinuityDetermine 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_________

Calculus

Limits & ContinuityWhich 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)

Calculus

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

Calculus

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

Calculus

Limits & ContinuityWrite an expression to match the statement below.
Add 5 to 48 divided by 12.

Calculus

Limits & ContinuityMiddle 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

Calculus

Limits & ContinuityFind 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

Calculus

Limits & ContinuityFind 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

Calculus

Limits & ContinuityFind 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

Calculus

Limits & ContinuityFor 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

Calculus

Limits & ContinuityHow 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.

Calculus

Limits & ContinuityThe 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)

Calculus

Limits & ContinuityFind 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.

Calculus

Limits & ContinuityFor 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

Calculus

Limits & ContinuityConsider 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.

Calculus

Limits & Continuityf(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?

Calculus

Limits & ContinuityFind an equation of the plane.
the plane through the points (0, 2, 2), (2, 0, 2), and (2, 2, 0)

Calculus

Limits & ContinuityConsider 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.