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mathematics
precalculus

Questions and Answers of Precalculus

Choose the statement that is not true. Assume b ≠ 0, c ≠ 0, and d ≠ 0 as necessary. (a) ac bc || (c) % - C d b ad bc bd (b) (d) 17918 음+ ac bd a + c b
The formula for the circumference C of a circle of radius r is _______.
The limit of a function y = f (x) as x approaches c is denoted by the symbol _______.
In Problems 41–58, fill in the blank(s) to form a correct inequality statement. If x ≤ 3, then 2.x 6.
Factor:(a) 2x2 − 10x.(b) x3 + 3x2 − 4x − 12
In the symbol n√a, the integer n is called the _______.
For x2 + Bx + C = ( x + a)( x + b), which of the following must be true?(a) ab = B and a + b = C(b) a + b = C and a − b = B(c) ab = C and a + b = B(d) ab = B and a − b = C
True or False The domain of any exponential function f (x) = ax, a > 0; a ≠ 1, is all real numbers.
The integral from a to b of f (x) is denoted by ______.
Solve the each equation(x − 2)(x2 + 2x + 4) = _______.
Choose the division problem that cannot be done using synthetic division.(a) 2x3 − 4x2 + 6x − 8 is divided by x − 8(b) x4 − 3 is divided by x + 1(c) x5 + 3x2 − 9x + 2 is divided by x +
In Problems 11–48, write each expression in the standard form a + bi.2i4 (1 + i2)
In Problems 43–52, find the limit as x approaches c of the average rate of change of each function from c to x.c = 3; f (x) = x3
In Problems 11 – 54, simplify each expression. Assume that all variables are positive when they appear. 93/24 - 381
In Problems 11 – 68, solve each equation. √√2t - 1 = 1
In Problems 37 – 54, perform the indicated operation and simplify the result. Leave your answer in factored form. 4 x - 1 2 x + 2
In Problems 43 – 54, factor each polynomial.x2 + 9x + 8
In Problems 29 – 48, add, subtract, or multiply, as indicated. Express your answer as a single polynomial in standard form.(x + 1)(x2 + 2x − 4)
In Problems 41–58, fill in the blank(s) to form a correct inequality statement. If x6, then - 2x - 12.
In Problems 11 – 54, simplify each expression. Assume that all variables are positive when they appear. (√x - 1) ²
In Problems 11–48, write each expression in the standard form a + bi.i6 + i4 + i2 + 1
In Problems 43 – 54, factor each polynomial.x2 + 7x + 10
Solve the each equation If f(x) {* 1 if x ≤ 0 if x > 0 what is f(0)?
In Problems 1 – 11, find the limit. lim√x² + 7 2 x-3
Rationalize the denominator of بنا 2 + √√3
True or Falsemeans -2)5 5 3 2 14 16 -10 -7 1 -32 -31
In Problems 1 – 11, find the limit. x - lim- x-1x3 1 1
True or False The LCM of 2x3 + 6x2 and 6x4 + 4x3 is 4x3(x + 1).
True or False The conjugate of 2 + 5i is − 2 − 5i.
In Problems 7–16, use a table to investigate the indicated limit. lim (4x³) x-2
Which pair of inequalities is equivalent to 0 < x ≤ 3 ? (a) x > 0 and x > 3. (c) x > 0 and x ≤ 3 (b) x < 0 and x > 3. (d) x < 0 and x ≤ 3
In Problems 7 – 12, use ZERO (or ROOT) to approximate the positive x-intercepts of each equation. Express each answer rounded to two decimal places.y = x3 + 3.2x2 − 16.83x − 5.31
True or False The slope of the tangent line to the graph of f at (c, f (c)) is the derivative of f at c.
Which of the following phrases best defines like radicals ?(a) Radical expressions that have the same index(b) Radical expressions that have the same radicand(c) Radical expressions that have the
True or False The polynomial x2 + 4 is prime.
If we approach c from only one side, then we have a(n)______ limit.
True or False Multiplying both sides of an equation by any number results in an equivalent equation_________.
True or False The degree of the product of two nonzero polynomials equals the sum of their degrees.
True or False All real numbers are complex numbers.
In Problems 1 – 11, find the limit. x²9 lim x-3x² x 12 -
In Problems 8 – 11, determine whether the statement is True or False if a < b and c < 0.a + c < b + c
True or False The velocity of an object whose position at time t is s (t) is the derivative s'(t).
To rationalize the denominator of the expressionmultiply both the numerator and the denominator by which of the following? √2 1-√3'
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.
In Problems 9–42, find each limit algebraically. lim x-1x² - 1 x² + x 2
In Problems 9 – 18, factor each polynomial by removing the common monomial factor.7x − 14
In Problems 9 – 18, factor each polynomial by removing the common monomial factor.3x2 − 3x
In Problems 11 – 54, simplify each expression. Assume that all variables are positive when they appear. √3x² √12x
In Problems 25–34, replace the question mark by < ,> or =, whichever is correct. 213 ? 0.67
In Problems 23–42, graph each function. Use the graph to investigate the indicated limit. lim f(x), f(x) = x-1 X
In Problems 33–42, use a graphing utility to approximate the derivative of each function at the given number.f (x) = 3x3 − 6x2 + 2 at −2
In Problems 33–44, find the one-sided limit. lim (2x+3) x→1+
In Problems 19 – 36, perform the indicated operation and simplify the result. Leave your answer in factored form. x² + 7x + 6 x²+x-6 -2 x2 + 5x – 6 करे x2 +5x+6
In Problems 29 – 48, add, subtract, or multiply, as indicated. Express your answer as a single polynomial in standard form.(6x5 + x3 + x) + (5x4 − x3 + 3x2)
In Problems 11 – 68, solve each equation.4z3 − 8z = 0
In Problems 9–42, find each limit algebraically. x4 lim x-1 x - 1 1
It takes a Xerox ColorQube 857dn laser printer 9 minutes longer to complete a 1440-page print job by itself than it takes a Brother HL-L8350CDW to complete the same job by itself. Together the two
In Problems 25–34, replace the question mark by < ,> or =, whichever is correct. 4 ? 0.25
In Problems 11–48, write each expression in the standard form a + bi.(1 − i)2
In Problems 11 – 54, simplify each expression. Assume that all variables are positive when they appear. √5x √20x3
In Problems 11 – 68, solve each equation. -2 x + 4 -3 x + 1
In Problems 19 – 36, perform the indicated operation and simplify the result. Leave your answer in factored form. 9x2 + 3x - 2 12x2 + 5x - 2 9x2 - 6x + 1 8x² - 10x - 3
In Problems 9–42, find each limit algebraically. x3 - 8 lim x-2x² - 4
In Problems 33–42, use a graphing utility to approximate the derivative of each function at the given number. f(x) = -5x4 + 9x + 3 x3 + 5x2 − 6 at -3
In Problems 11 – 54, simplify each expression. Assume that all variables are positive when they appear. 33 √10 4
In Problems 11–48, write each expression in the standard form a + bi.i14
In Problems 23–42, graph each function. Use the graph to investigate the indicated limit. lim f(x), f(x) = X - 1 3x1 if x < 0 if x ≥ 0
Solve the each equation We call 3√a the of a ________.
In Problems 33–44, find the one-sided limit. lim (3x² - 8) x-2+
In Problems 1–16, graph each equation using the following viewing windows:y = −x − 2 (a) Xmin=-5 Ymin =–4 Xmax = 5 Ymax = 4 Xscl = 1 Yscl = 1 (b) Xmin=-10 Ymin = _8 Xmax = 10 Ymax = 8 Xscl =
Solve the each equation lim A X-C ||
Ifexists, it is called the_________ of f at c. f(x) = f(c) X-C lim- X-C
If a function f does not approach a single number as x approaches c, then we say that lim f(x). x-c
In Problems 1–6, find each limit. lim x-1 x² - 4x - 5 2 x³ + 1 .3
In Problems 1–6, find each limit. lim x-1 4 tan x + cos²x
Choose the rational expression that simplifies to −1. a-b b - a (c) a + b a-b (a) (b) a-b a-b b-a b + a (d)
Choose the correct conclusion based on the following synthetic division:(a) x + 5 is a factor of 2x3 + 3x2 − 38x − 15(b) x − 5 is a factor of 2x3 + 3x2 − 38x − 15(c) x + 5 is not a factor
In Problems 1 – 11, find the limit. lim √1 - x² x-1-
A(n)_______ , denoted [a, b], consists of all real numbers x for which a ≤ x ≤ b.
In Problems 5–10, determine the viewing window used. NORMAL FLOAT AUTO REAL RADIAN MP -6 0 -6
Solve the each equation lim x X-C =
Solve the given equations.(a) 3√x3 = ______.(b) (4√x − 3 )4 = _________.
In Problems 1–6, find each limit. lim [(3x)(x - 2)²] x-5
Choose the best description of x2 − 64 .(a) Prime(b) Difference of two squares(c) Difference of two cubes(d) Perfect square
Name the trigonometric functions that have asymptotes.
The monomials that make up a polynomial are called which of the following?(a) Terms(b) Variables(c) Factors(d) Coefficients
Let n ≥ 2 and m ≥ 2 be integers, and let a and b be real numbers. Which of the following is not a property of radicals? Assume all radicals are defined. (a) (4-5 Na (c) Nab Nab (b) a + b = a +
In the complex number 5 + 2i, the number 5 is called the______ part; the number 2 is called________ the part; the number i is called the _______ _________.
In Problems 1 – 11, find the limit. lim x-1 x² + x + 2 x2 x² - 9
In Problems 1 – 11, find the limit. lim (5x + 6)3/2 x-2
Solve the each equation = ??
If Xmin = −4,Xmax = 12, and Xscl = 1, how should Y min, Y max, and Yscl be selected so that the viewing rectangle contains the point (4, 8) and the screen is square?
Choose the formula for the volume of a sphere of radius r. 4 (a) - ² (b) (c) 4 3 (d) 42
The_______ ________ states that the sense, or direction, of an inequality remains the same if each side is multiplied by a positive number, whereas the direction is reversed if each side is
If s = f (t) denotes the position of an object at time t, the derivative f'(t0) is the______ of the object at t0.
If a is a real number and n ≥ 2 is an integer, then which of the following expressions is equivalent to n√a, provided that it exists? (a) a-n (b) an (c) 1 an (d) a¹/n
Which of the following is not a case for determining congruent triangles?(a) Angle–Side–Angle(b) Side–Angle–Side(c) Angle–Angle–Angle(d) Side–Side–Side
Given 0 < a < b, which of the following is not the result of a reciprocal property? (a) 0 (d) 0 < 0 b
If a is a nonnegative real number, then which inequality statement best describes a ?(a) a < 0(b) a > 0(c) a ≤ 0(d) a ≥ 0
Choose the complete factorization of 4x2 − 8x − 60 .(a) 2 (x + 3)(x − 5)(b) 4 (x2 − 2x − 15)(c) (2x + 6)(2x − 10)(d) 4 (x + 3)(x − 5)

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