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mathematics
precalculus

Questions and Answers of Precalculus

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)
Let a and b be nonzero real numbers and m and n be integers. Which of the following is not a law of exponents? n (a) (²) = an bn am (c) = am-n an (b) (am)" = am+n (d) (ab)" anbn =
Two equations that have the same solution set are called ________ ________.
To complete the square of x2 + bx , use which of the following? (a) (2b)²(b) 26² (c) (b)² (d) b²
Choose the degree of the monomial 3x4 y2.(a) 3(b) 8(c) 6(d) 2
If Xmin = −6, Xmax = 10, and Xscl = 2, how should Y min, Y max, and Y scl be selected so that the viewing rectangle contains the point (4, 8) and the screen is square?
True or False The functionsand p(x) = x − 3 are equal. R(x) = 6-zx x + 3
In Problems 11 – 68, solve each equation. 3ܐ2 2 3 10 + x - 2 r + 5 (x + 5)(x – 2)
In Problems 37 – 54, perform the indicated operation and simplify the result. Leave your answer in factored form. X +
A gardener has 46 feet of fencing to be used to enclose a rectangular garden that has a border 2 feet wide surrounding it. See the figure.(a) If the length of the garden is to be twice its width,
In Problems 29 – 48, add, subtract, or multiply, as indicated. Express your answer as a single polynomial in standard form.− 2(x2 + x + 1) + (−5x2 − x + 2)
In Problems 9–42, find each limit algebraically. xXx 3 lim x-2 2x² + 4x 8 x² + x 6
In Problems 11–48, write each expression in the standard form a + bi.i−15
In Problems 33–42, use a graphing utility to approximate the derivative of each function at the given number. f(x)= x sinx at 7/3
In Problems 33–40, write each interval as an inequality involving x, and illustrate each inequality using the real number line.(4,∞)
In Problems 11 – 54, simplify each expression. Assume that all variables are positive when they appear. (3√6)(2√2)
In Problems 23–42, graph each function. Use the graph to investigate the indicated limit. lim f(x), f(x) = 3x if x ≤ 1 x + 1 if x > 1
In Problems 33–44, find the one-sided limit. lim sinx X-π/2+
In Problems 11 – 68, solve each equation. 1 2x + 3 + 1 x - 1 1 (2x + 3)(x - 1)
In Problems 37 – 54, perform the indicated operation and simplify the result. Leave your answer in factored form. x * la
In Problems 11 – 68, solve each equation.x3 + x2 − 20x = 0
In Problems 9–42, find each limit algebraically. lim x-1 x3 - x² + 3x - 3 x2 + 3x - 4
In Problems 33–42, use a graphing utility to approximate the derivative of each function at the given number. f(x) = x sinx at t|4
In Problems 11 – 54, simplify each expression. Assume that all variables are positive when they appear. (5√8)(-3√3)
In Problems 23–42, graph each function. Use the graph to investigate the indicated limit. lim f(x), f(x) = x-2 x2 2x if x ≤ 2 1 if x > 2
In Problems 9–42, find each limit algebraically. x³ + 2x² + x 3 + x3 + 2x + 2 lim x-1x4
In Problems 33–44, find the one-sided limit. lim (3 cos x) X-T
In Problems 11 – 68, solve each equation. x x - 2 + 3 = 2 x = 2
In Problems 37 – 54, perform the indicated operation and simplify the result. Leave your answer in factored form. x² 2x - 3 4 2x 3
In Problems 23–42, graph each function. Use the graph to investigate the indicated limit. limf(x), f(x) = x-0 X 1 3x if x < 0 if x = 0 if x > 0
A pond is enclosed by a wooden deck that is 3 feet wide. The fence surrounding the deck is 100 feet long.(a) If the pond is square, what are its dimensions?(b) If the pond is rectangular and the
In Problems 39–42, find the area of the shaded region. 2 2
In Problems 33–42, use a graphing utility to approximate the derivative of each function at the given number. f(x) = x² sinx at F|3
In Problems 11–48, write each expression in the standard form a + bi.i−23
In Problems 11 – 54, simplify each expression. Assume that all variables are positive when they appear. 3√2 + 4√2
In Problems 33–44, find the one-sided limit. lim x-2+ x2 x² - 4 x - 2
In Problems 9–42, find each limit algebraically. lim x3 x3 3x² + 4x - 12 x43x³ + x 3
In Problems 37 – 42, factor the sum or difference of two cubes.x3 + 125
In Problems 39–42, find the area of the shaded region. 2 C 2
In Problems 11 – 68, solve each equation. 2x x + 3 || -6 x+3 2
In Problems 33–42, use a graphing utility to approximate the derivative of each function at the given number. f(x)= x² sinx at t|4
In Problems 11 – 54, simplify each expression. Assume that all variables are positive when they appear. 6√5 - 4√5
In Problems 23–42, graph each function. Use the graph to investigate the indicated limit. lim f(x), f(x) = x-0 { 1 -1 if x < 0 if x > 0
In Problems 33–44, find the one-sided limit. x3 X lim x-1- x - 1
In Problems 29 – 48, add, subtract, or multiply, as indicated. Express your answer as a single polynomial in standard form.(x2 − x + 2) + (2x2 − 3x + 5) − (x2 + 1)
In Problems 11–48, write each expression in the standard form a + bi.4 + i3
In Problems 37 – 54, perform the indicated operation and simplify the result. Leave your answer in factored form. x + 1 x - 3 + 2x x - 3 3
In Problems 9–42, find each limit algebraically. √√x - √2 lim. x-2 x - 2
In Problems 35–40, write each statement as an inequality.x is greater than or equal to 2
In Problems 37 – 42, factor the sum or difference of two cubes.27 − 8x3
In Problems 39–42, find the area of the shaded region. 2 2
In Problems 29 – 48, add, subtract, or multiply, as indicated. Express your answer as a single polynomial in standard form.(x2 + 1) − (4x2 + 5) + (x2 + x − 2)
In Problems 11–48, write each expression in the standard form a + bi.6i3 − 4i5
In Problems 37 – 54, perform the indicated operation and simplify the result. Leave your answer in factored form. 2х - 5 3x + 2 + x +4 3x + 2
In Problems 41–58, fill in the blank(s) to form a correct inequality statement. If x < 5, then x - 5. 0.
In Problems 11 – 54, simplify each expression. Assume that all variables are positive when they appear. -√18 + 2√8
In Problems 23–42, graph each function. Use the graph to investigate the indicated limit. lim f(x), f(x) = sinx x² if x ≤ 0 if x > 0
In Problems 33–44, find the one-sided limit. lim x-1- x³ + 1 x2 1 3
In Problems 9–42, find each limit algebraically. √x - √5 lim- x-5 x - 5
In Problems 11 – 54, simplify each expression. Assume that all variables are positive when they appear. 2√12 - 3√27
In Problems 39–42, find the area of the shaded region. 2
In Problems 41–58, fill in the blank(s) to form a correct inequality statement. If x < -4, then x + 4. 0.
In Problems 33–44, find the one-sided limit. x³x² lim x=0+ x4 + x² 2
In Problems 33–42, use a graphing utility to approximate the derivative of each function at the given number.f (x) = ex sin x at 2
In Problems 37 – 42, factor the sum or difference of two cubes.8x3 + 27
In Problems 23–42, graph each function. Use the graph to investigate the indicated limit. ex -{it, lim f(x), f(x) = x-0 if x > 0 1- x if x < 0
In Problems 11 – 54, simplify each expression. Assume that all variables are positive when they appear. (√3+3)(√3-1)
In Problems 11 – 68, solve each equation.x3 + 6x2 − 7x = 0
In Problems 37 – 54, perform the indicated operation and simplify the result. Leave your answer in factored form. 3x + 5 2х - 1 2х - 4 2x - 1
In Problems 11–48, write each expression in the standard form a + bi.4i3 − 2i2 + 1
In Problems 43 and 44, an integral is given.(a) What area does the integral represent?(b) Graph the function, and shade the region represented by the integral.(c) Use a graphing utility to
In Problems 41–58, fill in the blank(s) to form a correct inequality statement. If x>-4, then x + 4. 0.
In Problems 37 – 54, perform the indicated operation and simplify the result. Leave your answer in factored form. 5x – 4 3x + 4 x+1 3x + 4
In Problems 33–44, find the one-sided limit. lim x-2+ x² + x - 2 x² + 2x
In Problems 33–42, use a graphing utility to approximate the derivative of each function at the given number.f (x) = e−x sin x at 2
In Problems 43 and 44, an integral is given.(a) What area does the integral represent?(b) Graph the function, and shade the region represented by the integral.(c) Use a graphing utility to
In Problems 43–48, use a graphing utility to investigate the indicated limit. Round answers to two decimal places. x3 - x² x² + x lim x-1x4 x³ + 2x - 3
In Problems 43–48, use a graphing utility to investigate the indicated limit. Round answers to two decimal places. x³ + x² + 3x + 3 -3 lim x-1x4 + x³ + 2x + 2
In Problems 37 – 42, factor the sum or difference of two cubes.64 − 27x3
In Problems 33–44, find the one-sided limit. lim x--4- x² + x - 12 x² + 4x
In Problems 11 – 68, solve each equation.x3 + x2 − x − 1 = 0
In Problems 41–58, fill in the blank(s) to form a correct inequality statement. If x > 6, then x - 6. 0.
In Problems 11 – 54, simplify each expression. Assume that all variables are positive when they appear. (√5-2)(√5 + 3)
In Problems 43–48, use a graphing utility to investigate the indicated limit. Round answers to two decimal places. x3 x³ lim x-2 2x² + 4x - 8 x² + x - 6
In Problems 43 – 54, factor each polynomial.x2 + 5x + 6
In Problems 37 – 54, perform the indicated operation and simplify the result. Leave your answer in factored form. 4 x-2 + X 2 - x
In Problems 11 – 68, solve each equation.x3 + 4x2 − x − 4 = 0
In Problems 41–58, fill in the blank(s) to form a correct inequality statement. If x4, then 3x. -12.
In Problems 11 – 54, simplify each expression. Assume that all variables are positive when they appear. 5³/2 - 23/54
In Problems 43 – 54, factor each polynomial.x2 + 6x + 8
In Problems 29 – 48, add, subtract, or multiply, as indicated. Express your answer as a single polynomial in standard form.−2x2 (4x3 + 5)
In Problems 11 – 68, solve each equation.2x3 + 4 = x2 + 8x
The purity of gold is measured in karats, with pure gold being 24 karats. Other purities of gold are expressed as proportional parts of pure gold. Thus, 18-karat gold is 18/24, or 75% pure gold;
In Problems 43 – 54, factor each polynomial.x2 + 7x + 6
In Problems 29 – 48, add, subtract, or multiply, as indicated. Express your answer as a single polynomial in standard form.5x3 (3x − 4)

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