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mathematics
precalculus

Questions and Answers of Precalculus

Graph the numbers x on the real number line. x > -1
Graph the numbers x on the real number line. x < 4
Graph the numbers x on the real number line. X ≥ -2
Write each statement as an inequality.x is greater than or equal to 2
Write each statement as an inequality.x is less than or equal to 1
Write each statement as an inequality.y is greater than -5
Write each statement as an inequality.x is less than 2
Write each statement as an inequality.z is negative
Write each statement as an inequality.x is positive
Replace the question mark by <, > or = whichever is correct.1/4 ? 0.25
Replace the question mark by <, > or = whichever is correct.2/3 ? 0.67
Replace the question mark by <, > or = whichever is correct.1/3 ? 0.33
Replace the question mark by <, > or = whichever is correct.1/2 ? 0.5
Replace the question mark by <, > or = whichever is correct.√2 ? 1.41
Replace the question mark by <, > or = whichever is correct.π ? 3.14
Replace the question mark by <, > or = whichever is correct.-3 ? -5/2
Replace the question mark by <, > or = whichever is correct.-1 ? -2
Replace the question mark by <, > or = whichever is correct.5 ? 6
Replace the question mark by <, > or = whichever is correct.1/2 ? 0
On the real number line, label the points with coordinates 0, -2, 2, -1.5, 3/2, 1/3 and 2/3.
On the real number line, label the points with coordinates 0, 1, -1, -2.5, 3/4 and 0.25.
Use U universal set = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}, A = {1, 3, 4, 5, 9}, and C = {1,3,4,6} to find the set. (A̅ ∩ B̅)
Use U universal set = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}, A = {1, 3, 4, 5, 9}, and C = {1,3,4,6} to find the set. (A̅ ∪ B̅)
Use U universal set = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}, A = {1, 3, 4, 5, 9}, and C = {1,3,4,6} to find the set. BUC
Use U universal set = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}, A = {1, 3, 4, 5, 9}, and C = {1,3,4,6} to find the set. ANB
Use U universal set = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}, A = {1, 3, 4, 5, 9}, and C = {1,3,4,6} to find the set. C̅
Use U universal set = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}, A = {1, 3, 4, 5, 9}, and C = {1,3,4,6} to find the set. A̅
Use U universal set = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}, A = {1, 3, 4, 5, 9}, and C = {1,3,4,6} to find the set. (A ∩ B) ∪ C
Use U universal set = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}, A = {1, 3, 4, 5, 9}, and C = {1,3,4,6} to find the set. (A ∪ B) ∩ C
Use U universal set = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}, A = {1, 3, 4, 5, 9}, and C = {1,3,4,6} to find the set. A ∩ C
Use U universal set = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}, A = {1, 3, 4, 5, 9}, and C = {1,3,4,6} to find the set. A ∩ B
Use U universal set = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}, A = {1, 3, 4, 5, 9}, and C = {1,3,4,6} to find the set. A ∪ C
Use U universal set = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}, A = {1, 3, 4, 5, 9}, and C = {1,3,4,6} to find the set. A ∪ B
True or False.To multiply two expressions having the same base, retain the base and multiply the exponents.
True or False.The absolute value of a real number is always greater than zero.
True or False.The distance between two distinct points on the real number line is always greater than zero.
True or False.The product of two negative real numbers is always greater than zero.
In the expression 24, the number 2 is called the______and 4 is called the_______.
An inequality of the form a > b is called a(n)________inequality.
On the real number line, the real number zero is the coordinate of the _______.
A(n) ______is a letter used in algebra to represent any number from a given set of numbers
A particle is moving along a straight line according to some position function s(t). The distance (in feet) of the particle, s, from its starting point after t seconds is given in the table. Find the
Write the integral that represents the shaded area. Do not attempt to evaluate. УА 8 f(x) = -x + 5x + 3 4 8
The function is defined on the interval [0, 4].(a) Graph f.(b) Partition [0, 4] into eight subintervals of equal length and choose u as the left endpoint of each subinterval. Use the
For the function f(x) = 4x2 – 11x – 3:(a) Find the derivative of f at x = 2.(b) Find the equation of the tangent line to the graph of f at the point (2, -9).(c) Graph f and the tangent line.
Determine where the rational function is undefined. Determine whether an asymptote or a hole appears at such numbers. 4x x + 6x? – 4r – 24 R(x) x + 5x – 14 %3D
Use the accompanying graph of y = f(x). Determine whether f is continuous at each of the following numbers. If it is not, explain why not. (a) x = -2(b) x = 1(c) x = 3 (d) x = 4 УА
Use the accompanying graph of y = f(x). Does exist? If so, what is it? If not, explain why not. УА -4 4 4, 4. lim f(x)
Use the accompanying graph of y = f(x). Find УА -4 4 4, 4. lim f(x)
Use the accompanying graph of y = f(x). Find УА -4 4 4, 4. lim f(x) 3'
Use the accompanying graph of y = f(x). Find
Determine the value for k that will make the function continuous at c = 4. x? – 9 x + 3 kx + 5 if x > 4 if x < 4 f(x) =
Find the limit. tan x lim r→1 + cos².x
Find the limit. lim (3x)(x – 2)2]|
Find the limit. Find each limit. x — 4х — 5 х + 1 lim х>-1
Find the limit. lim V7 - 3x
Find the limit.
Find the limit. lim (-x + 3x – 5) x² + 3x · lim Зх
An integral is given. (a) What area does the integral represent? (b) Provide a graph that illustrates this area. (c) Use a graphing utility to approximate this area. -2п/3 sin x
An integral is given. (a) What area does the integral represent? (b) Provide a graph that illustrates this area. (c) Use a graphing utility to approximate this area. Г- e* dx J-1
An integral is given. (a) What area does the integral represent? (b) Provide a graph that illustrates this area. (c) Use a graphing utility to approximate this area. Vx dx
An integral is given. (a) What area does the integral represent? (b) Provide a graph that illustrates this area. (c) Use a graphing utility to approximate this area. (9 — х')
A function is defined over an interval [a, b].(a) Graph indicating the area A under from a to b. (b) Approximate the area A by partitioning [a, b] into three subintervals of equal length and
A function is defined over an interval [a, b].(a) Graph indicating the area A under from a to b. (b) Approximate the area A by partitioning [a, b] into three subintervals of equal length and
A function is defined over an interval [a, b].(a) Graph indicating the area A under from a to b. (b) Approximate the area A by partitioning [a, b] into three subintervals of equal length and
A function is defined over an interval [a, b].(a) Graph indicating the area A under from a to b. (b) Approximate the area A by partitioning [a, b] into three subintervals of equal length and
Repeat Problem 75 for f(x) = -2x + 9.Data From problem 75.The function f(x) = 2x + 3 is is defined on the interval [0, 4].(a) Graph In (b)–(e), approximate the area A under from to as
The function f(x) = 2x + 3 is is defined on the interval [0, 4].(a) Graph In (b)–(e), approximate the area A under from to as follows: (b) Partition [0, 4] into four subintervals of equal
The following data represent the distance s (in feet) that a parachutist has fallen over time t (in seconds). (a) Find the average speed from t = 1 to t = 4 seconds. (b) Find the average
The following data represent the revenue R (in dollars) received from selling x wristwatches at Wilk’s Watch Shop(a) Find the average rate of change of revenue from x = 25 to x = 130
The area A of a circle is πr2. Find the instantaneous rate of change of area with respect r at r = 2 feet. What is the average rate of change from r = 2 to r = 3? What is the average rate of change
In physics, it is shown that the height s of a ball thrown straight up with an initial speed of 96 ft sec from a rooftop 112 feet high iss = s(t) = -16 t2 + 96t + 112where t is the elapsed time that
Find the derivative of each function at the number indicated using a graphing utility.f(x) = x secx at π/6
Find the derivative of each function at the number indicated using a graphing utility.f(x) = x3 tanx at π/6
Find the derivative of each function at the number indicated using a graphing utility. -6x + 9x – 2 at 5 8x2 + 6x – 1 f(x)
Find the derivative of each function at the number indicated using a graphing utility.f(x) = 4x4 – 3x3 + 6x – 9 at -2
Find the derivative of each function at the number indicated. f(x) = 3x2 – 4x + 1 at 2
Find the derivative of each function at the number indicated. f(x) = 2x2 + 3x + 2 at 1
Find the derivative of each function at the number indicated. f(x) = 2x2 + 4x at -1
Find the derivative of each function at the number indicated. f(x) = x2 – 3x at 0
Find the derivative of each function at the number indicated. f(x) = -4 + 3x2 at 1
Find the derivative of each function at the number indicated. f(x) = -4x2 + 5 at 3
Find the slope of the tangent line to the graph of at the given point. Graph and the tangent line. f(x) = x3 – x2 at (1, 0)
Find the slope of the tangent line to the graph of at the given point. Graph and the tangent line. f(x) = x3 + x2 at (2, 12)
Find the slope of the tangent line to the graph of at the given point. Graph and the tangent line. f(x) = 2x2 + 5x – 3 at (1, 4)
Find the slope of the tangent line to the graph of at the given point. Graph and the tangent line. f(x) = x2 + 2x – 3x – 3 at (-1, -4)
Find the slope of the tangent line to the graph of at the given point. Graph and the tangent line. f(x) = 3x2 – 6x at (0, 0)
Find the slope of the tangent line to the graph of at the given point. Graph and the tangent line. f(x) = 2x2 + 8x at (1, 10)
Determine where each rational function is undefined. Determine whether an asymptote or a hole appears at such numbers. x' + 3x – 2x – 6 R(x) x² + x – 6
Determine where each rational function is undefined. Determine whether an asymptote or a hole appears at such numbers. x' - 2x? + 4x – 8 R(x) x? - 11x + 18
Discuss whether R is continuous at c. Use limits to analyze the graph of R at c. 3x2 + 6x at c = -2 and c = 2 R(x)
Discuss whether R is continuous at c. Use limits to analyze the graph of R at c. x + 4 R(x) at c = -4 and c = 4 2 – 16 х
Use the accompanying graph of y = f(x).Is f continuous at 5? УА 4 (-2, 2) (-6, 2) • (-4, 1) -6 -4 -2 4 -2 -4
Use the accompanying graph of y = f(x).Is f continuous at 4? УА 4 (-2, 2) (-6, 2) • (-4, 1) -6 -4 -2 4 -2 -4
Use the accompanying graph of y = f(x).Is f continuous at 2? УА 4 (-2, 2) (-6, 2) • (-4, 1) -6 -4 -2 4 -2 -4
Use the accompanying graph of y = f(x).Is f continuous at 0? УА 4 (-2, 2) (-6, 2) • (-4, 1) -6 -4 -2 4 -2 -4
Use the accompanying graph of y = f(x).Is f continuous at -4? УА 4 (-2, 2) (-6, 2) • (-4, 1) -6 -4 -2 4 -2 -4
Use the accompanying graph of y = f(x).Is f continuous at -2? УА 4 (-2, 2) (-6, 2) • (-4, 1) -6 -4 -2 4 -2 -4
Use the accompanying graph of y = f(x).Does exist? If it does, what is it? lim f(x) УА 4 (-2, 2) (-6, 2) • (-4, 1) -6 -4 -2 4 -2 -4
Use the accompanying graph of y = f(x).Does exist? If it does, what is it? lim f(x) УА 4 (-2, 2) (-6, 2) • (-4, 1) -6 -4 -2 4 -2 -4

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