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mathematics
precalculus

Questions and Answers of Precalculus

In Problems 8 – 11, determine whether the statement is True or False if a < b and c < 0. a C V C
In Problems 11 – 54, simplify each expression. Assume that all variables are positive when they appear. 3/27
In Problems 7–16, use a table to investigate the indicated limit. 2 x² - 9 3x lim x-3 x2
In Problems 9–20, find the slope of the tangent line to the graph of f at the given point. Graph f and the tangent line.f (x) = x2 + 2 at (−1, 3)
In Problems 9–42, find each limit algebraically. lim x x--3
In Problems 11 – 54, simplify each expression. Assume that all variables are positive when they appear. 4/16
In Problems 8–12, use the graph of y = f (x).Determine whether f is continuous at each of the followingnumbers. If it is not, explain why not.(a) x = −2(b) x = 1(c) x = 3(d) x = 4 -4 у -4 4 X
In Problems 9 – 18, factor each polynomial by removing the common monomial factor.ax2 + a
In Problems 7 – 18, reduce each rational expression to lowest terms. x² 2 + 4x + 4 x2 x² - 4
In Problems 11 – 68, solve each equation.2x − 3 = 5
In Problems 12 – 15, determine whether f is continuous at c. f(x) = x² - 4 x2 x + 2 c = -2 C
In Problems 12 – 15, determine whether f is continuous at c.f (x) = 3x4 − x2 + 2, c = 5
In Problems 9–42, find each limit algebraically. lim (5x) x--2
In Problems 11–22, use U = universal set = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}, A = {1, 3, 4, 5, 9}, B = {2, 4, 6, 7, 8}, and C = {1, 3, 4, 6} to find each set. An B
In Problems 11 – 16, select a setting so that each of the given points will lie within the viewing rectangle.(5, 0), (6, 8), (−2, −3)
In Problems 7–16, use a table to investigate the indicated limit. lim (ex + 1) x-0
In Problems 11 – 54, simplify each expression. Assume that all variables are positive when they appear. V8
In Problems 9–20, find the slope of the tangent line to the graph of f at the given point. Graph f and the tangent line.f (x) = 3 − x2 at (1, 2)
In Problems 9 – 18, factor each polynomial by removing the common monomial factor.ax − a
In Problems 11 – 68, solve each equation.3x + 4 = −8
In Problems 9–20, find the slope of the tangent line to the graph of f at the given point. Graph f and the tangent line.f (x) = 3x2 at (2, 12)
In Problems 7 – 18, reduce each rational expression to lowest terms. 3у2 - у - 2 y - 3у2 + 5у + 2
In Problems 9–42, find each limit algebraically. lim (-3x) x-4
In Problems 12 – 15, determine whether f is continuous at c. f(x) = x² - 4 x + 2 4 if x = -2 if x -2 C c = -2
In Problems 7–16, use a table to investigate the indicated limit. lim x-0 ex - e-x 2
In Problems 7 – 18, reduce each rational expression to lowest terms. y² - 25 2y²8y-10
In Problems 11 – 68, solve each equation. ادی x = 5 12
In Problems 11 – 54, simplify each expression. Assume that all variables are positive when they appear. 二
In Problems 11–22, use U = universal set = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}, A = {1, 3, 4, 5, 9}, B = {2, 4, 6, 7, 8}, and C = {1, 3, 4, 6} to find each set. Anc
In Problems 9 – 18, factor each polynomial by removing the common monomial factor.x3 + x2 + x
In Problems 9 – 18, factor each polynomial by removing the common monomial factor.x3 − x2 + x
In Problems 9–42, find each limit algebraically. lim (3x + 2) x-2
In Problems 7–16, use a table to investigate the indicated limit. cosx – 1 1, x in radians X lim. x-0
In Problems 12 – 15, determine whether f is continuous at c. f(x) = x² - 4 x + 2 -4 if x = if x = -2 -2 C c = -2
In Problems 11 – 68, solve each equation. 2/3 X = 9 2
In Problems 9 – 18, tell whether the expression is a monomial. If it is, name the variable(s) and the coefficient, and give the degree of the monomial. If it is not a monomial, state why not.−2xy2
In Problems 9 – 18, tell whether the expression is a monomial. If it is, name the variable(s) and the coefficient, and give the degree of the monomial. If it is not a monomial, state why
In Problems 11 – 54, simplify each expression. Assume that all variables are positive when they appear.
In Problems 9 – 18, tell whether the expression is a monomial. If it is, name the variable(s) and the coefficient, and give the degree of the monomial. If it is not a monomial, state why not. 8x y
In Problems 7 – 18, reduce each rational expression to lowest terms. x² + 4x - 5 x² - 2x + 1
In Problems 7–16, use a table to investigate the indicated limit. lim tan x x-0 X x in radians
In Problems 9–42, find each limit algebraically. lim (2 - 5x) x-3
In Problems 11 – 54, simplify each expression. Assume that all variables are positive when they appear. √75
In Problems 9–20, find the slope of the tangent line to the graph of f at the given point. Graph f and the tangent line.f (x) = 2x2 + x at (1, 3)
In Problems 9 – 18, factor each polynomial by removing the common monomial factor.2x2 − 2x
In Problems 9–42, find each limit algebraically. lim (3x² - 5x) x--1
In Problems 11 – 54, simplify each expression. Assume that all variables are positive when they appear. 700
In Problems 7 – 18, use synthetic division to find the quotient and remainder when:0.1x3 + 0.2x is divided by x + 1.1
In Problems 7 – 18, reduce each rational expression to lowest terms. 2-x + 2x zx - x
In Problems 11 – 68, solve each equation.6 − x = 2x + 9
In Problems 11–22, use U = universal set = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}, A = {1, 3, 4, 5, 9}, B = {2, 4, 6, 7, 8}, and C = {1, 3, 4, 6} to find each set. А
In Problems 7 – 18, use synthetic division to find the quotient and remainder when:0.1x2 − 0.2 is divided by x + 2.1
In Problems 9–20, find the slope of the tangent line to the graph of f at the given point. Graph f and the tangent line.f (x) = 3x2 − x at (0, 0)
In Problems 7 – 18, reduce each rational expression to lowest terms. x2 + 5x – 14 2- x
In Problems 9–42, find each limit algebraically. lim (8x² - 4) x-2
In Problems 11 – 68, solve each equation.3 − 2x = 2 − x
In Problems 9–20, find the slope of the tangent line to the graph of f at the given point. Graph f and the tangent line.f (x) = x2 − 2x + 3 at (−1, 6)
In Problems 13–32, use the accompanying graph of y = f(x).Find f (2) and f (6). x = −6 (-4,2) -8 -6 -4 -2 y, 4 2 -2 -4 I 2 (2,3) 6 (6,2) X
In Problems 11 – 54, simplify each expression. Assume that all variables are positive when they appear. √45x3
In Problems 7 – 18, reduce each rational expression to lowest terms. 2x² + 5x 3 – 1 - 2x
In Problems 9–42, find each limit algebraically. lim (5x43x2 + 6x - 9) x→1
In Problems 13–22, a function f is nonnegative and continuous on an interval [a, b].(a) Graph f, indicating the area A under f from a to b.(b) Approximate the area A by partitioning [a, b] into
In Problems 9 – 18, factor each polynomial by removing the common monomial factor.3x2 y − 6xy2 + 12xy
In Problems 9 – 18, tell whether the expression is a monomial. If it is, name the variable(s) and the coefficient, and give the degree of the monomial. If it is not a monomial, state why not.x2 + y2
In Problems 11 – 68, solve each equation.2 (3 + 2x) = 3( x − 4)
In Problems 11 – 54, simplify each expression. Assume that all variables are positive when they appear. 3/32
In Problems 13 – 18, the lengths of the legs of a right triangle are given. Find the hypotenuse.a = 14, b = 48
In Problems 9–20, find the slope of the tangent line to the graph of f at the given point. Graph f and the tangent line.f (x) = −2x2 + x − 3 at (1, −4)
In Problems 11–22, use U = universal set = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}, A = {1, 3, 4, 5, 9}, B = {2, 4, 6, 7, 8}, and C = {1, 3, 4, 6} to find each set. An B
In Problems 9 – 18, factor each polynomial by removing the common monomial factor.60x2 y − 48xy2 + 72x3y
In Problems 7 – 18, use synthetic division to find the quotient and remainder when:x5 + 1 is divided by x + 1
In Problems 19–24, an inequality is given. Write the inequality obtained by:(a) Adding 3 to each side of the given inequality.(b) Subtracting 5 from each side of the given inequality.(c)
In Problems 9–20, find the slope of the tangent line to the graph of f at the given point. Graph f and the tangent line.f (x) = x3 + x at (2, 10)
In Problems 19 – 26, factor the difference of two squares.x2 − 1
In Problems 13–32, use the accompanying graph of y = f(x). x = −6 (-4,2) -8 -6 -4 -2 y, 4 2 -2 -4 I 2 (2,3) 6 (6,2) X
In Problems 16 – 27, use the accompanying graph of y = f (x).Find f (−6) and f (−4). (-6, 2) | -6 م (-2,2) .(-4,1) -2 -4 ۷۸ 4 2 -O-2 -4 2 ا 4 ه X
In Problems 9–42, find each limit algebraically. lim (8x5 x-1 - 7x3 +8x2 + x -4)
In Problems 11 – 54, simplify each expression. Assume that all variables are positive when they appear. 3√/54
Betsy, a recent retiree, requires $2100 per year in extra income. She has $50,000 to invest and can invest in B-rated bonds paying 6% per year or in a certificate of deposit (CD) paying 1.2% per
In Problems 11–22, use U = universal set = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}, A = {1, 3, 4, 5, 9}, B = {2, 4, 6, 7, 8}, and C = {1, 3, 4, 6} to find each set. BUC
In Problems 19–24, an inequality is given. Write the inequality obtained by:(a) Adding 3 to each side of the given inequality.(b) Subtracting 5 from each side of the given inequality.(c)
In Problems 9–20, find the slope of the tangent line to the graph of f at the given point. Graph f and the tangent line.f (x) = x3 − x2 at (1, 0)
In Problems 13–32, use the accompanying graph of y = f(x). x = −6 (-4,2) -8 -6 -4 -2 y, 4 2 -2 -4 I 2 (2,3) 6 (6,2) X
In Problems 19 – 26, factor the difference of two squares.x2 − 4
In Problems 9–42, find each limit algebraically. lim(x² + 1)³ 3 x-1
In Problems 16 – 27, use the accompanying graph of y = f (x). (-6, 2) | -6 م (-2,2) .(-4,1) -2 -4 ۷۸ 4 2 -O-2 -4 2 ا 4 ه X
After 2 years, Betsy (see Problem 19 ) finds that she will now require $2700 per year. Assuming that the remaining information is the same, how should the money be reinvested?Data from problem
In Problems 11 – 68, solve each equation.5 − (2x − 1) = 10
In Problems 11 – 54, simplify each expression. Assume that all variables are positive when they appear. V-8r4
In Problems 11–22, use U = universal set = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}, A = {1, 3, 4, 5, 9}, B = {2, 4, 6, 7, 8}, and C = {1, 3, 4, 6} to find each set. AUB
In Problems 19–24, an inequality is given. Write the inequality obtained by:(a) Adding 3 to each side of the given inequality.(b) Subtracting 5 from each side of the given inequality.(c)
In Problems 19 – 26, factor the difference of two squares.4x2 − 1
In Problems 13–32, use the accompanying graph of y = f(x). x = −6 (-4,2) -8 -6 -4 -2 y, 4 2 -2 -4 I 2 (2,3) 6 (6,2) X
In Problems 9–42, find each limit algebraically. lim(3x - 4)² x-2
In Problems 17–22, use the graph shown to investigate the indicated limit. lim f(x) x-4 YA 8 6 69 4 2 4 8 X
In Problems 13–32, use the accompanying graph of y = f(x). x = −6 (-4,2) -8 -6 -4 -2 y, 4 2 -2 -4 I 2 (2,3) 6 (6,2) X
In Problems 9–42, find each limit algebraically. lim √5x + 4 x-1
On the real number line, label the points with coordinates 0, 1, −1, 2, -2.5, 2, a 3 and 0.25.
In Problems 13–32, use the accompanying graph of y = f(x). x = −6 (-4,2) -8 -6 -4 -2 y, 4 2 -2 -4 I 2 (2,3) 6 (6,2) X
In Problems 9–42, find each limit algebraically. lim √1 - 2x x-0

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