Questions and Answers of Calculus Graphical, Numerical, Algebraic

In Exercises (a) write a formula for ∫ o g and g o ∫ and find the (b) domain and (c) range of each. f(x) = 2x², g(x)=√x+2
Let x = a sec t and y = b tan t.(a) Let a = 1, 2, or 3, b = 1,2, or 3, and graph using the parameter interval (-π/2, π/2). Explain what you see, and describe the role of a and b in these parametric
In Exercises find a formula for ∫-1 and verify that (∫ o ∫-1) (x) = (∫-1 o ∫) (x) = x. f(x)= 100 1+2-*
In Exercises find a formula for ∫-1 and verify that (∫ o ∫-1) (x) = (∫-1 o ∫) (x) = x. f(x) = 50 1 + 1.1-*
In Exercises write a piecewise formula for the function. 34 2 -3 (2.-1)
Which of the following gives the domain of y = 2e -x- 3?(A) (-∞, ∞) (B) [-3, ∞) (C) [-1, ∞) (D) (- ∞, 3](E) x ≠ 0
A car starts from point P at time / = 0 and travels at 45 mph.(a) Write an expression d(t) for the distance the car travels from P.(b) Graph y = d(t).(c) What is the slope of the graph in (b)? What
Use the equation of Exercise 43 to approximate the answers to the following questions about the temperatures in Fairbanks, Alaska, shown in the figure in Exercise 43. Assume that the year has 365
In Exercises (a) write a formula for ∫ o g and g o ∫ and find the (b) domain and (c) range of each. f(x)=√x, g(x) = VI-x
Prove that the function ∫ is its own inverse(a) ∫(x) = √1 - x2, x ≥ 0 (b) ∫(x) = 1/x
In Exercises write a piecewise formula for the function. (-1, 1) (1.1) 14 3
Which of the following gives the range of y = 4 - 2-x?(A) (- ∞, ∞) (B) (- ∞, 4) (C) [- 4, ∞)(D) (- ∞, 4] (E) All reals
Table 1.2 shows the mean annual compensation of construction workers.(a) Find the linear regression equation for the data.(b) Find the slope of the regression line. What does the slope
In Exercises a parametrization is given for a curve.(a) Graph the curve. Identify the initial and terminal points, if any. Indicate the direction in which the curve is traced.(b) Find a Cartesian
In Exercises write a piecewise formula for the function. 2 (-2,-1) (1,-1) (3,-1)
The half-life of a certain radioactive substance is 12 hours. There are 8 grams present initially.(a) Express the amount of substance remaining as a function of time t.(b) When will there be 1 gram
Table 1.3 lists the ages and weights of nine girls.(a) Find the linear regression equation for the data.(b) Find the slope of the regression line. What does the slope represent?(c) Superimpose the
Which of the following gives the best approximation for the zero of ∫(x) = 4 - ex? (A) x = -1.386 (B) x = 0.386 (C) x = 1.386(D) x = 3 (E) There are no zeros
In Exercises a parametrization is given for a curve.(a) Graph the curve. Identify the initial and terminal points, if any. Indicate the direction in which the curve is traced.(b) Find a Cartesian
In Exercises write a piecewise formula for the function. T 2 (T. 1) T
Determine how much time is required for a $500 investment to double in value if interest is earned at the rate of 4.75% compounded annually.
Let y1 = x2 and y2 = 2X.(a) Graph y1 and y2 in [-5, 5] by [-2, 10]. How many times do you think the two graphs cross?(b) Compare the corresponding changes in y1 and y2 as x changes from 1 to 2,
In Exercises a parametrization is given for a curve.(a) Graph the curve. Identify the initial and terminal points, if any. Indicate the direction in which the curve is traced.(b) Find a Cartesian
True or False The slope of a vertical line is zero. Justify your answer.
In Exercises write a piecewise formula for the function. A 0 -А Т 1 Т T 3T 2T
The population of Glenbrook is 375,000 and is increasing at the rate of 2.25% per year. Predict when the population will be 1 million.
In Exercises assume that the graph of the exponential function ∫(x) = k. ax passes through the two points. Find the values of a and k.(1, 4.5), (-1, 0.5)
True or False The slope of a line perpendicular to the line y = mx + b is /m. Justify your answer.
Give a convincing argument that the period of tan x is π.
Which of the following is an equation of the line through ( -3, 4) with slope 1/2?(A) y - 4 =| (x + 3) (B) y + 3 =| (x - 4)(C) y - 4 = - 2(x + 3) (D) y - 4 = 2(x + 3)(E) y + 3 = 2(x - 4)
In Exercises (a) draw the graph of the function. Then find its (b) domain and (c) range.∫(x) = -|3 - x| + 2
In Exercises let x = 0 represent 1990, x = 1 represent 1991, and so forth.(a) Find a natural logarithm regression equation for the data in Table 1.16 and superimpose its graph on a scatter plot of
In Exercises a parametrization is given for a curve.(a) Graph the curve. Identify the initial and terminal points, if any. Indicate the direction in which the curve is traced.(b) Find a Cartesian
In Exercises find the limits. lim e sinx 40
In Exercises letFind a value of c for which the equation ∫(x) = c has no solution. f(x) = 5-x, x≤3 -x² + 6x8, x> 3.
In Exercises write a formula for (a) ∫(- x) and (b) ∫(1/x). Simplify where possible. ƒ(x) = (x + ¹) s sin x
In Exercises find the points of continuity and the points of discontinuity of the function. Identify each type of discontinuity.y = In (x + 1)
For what value of b will the slope of the line through (2, 3) and (4, b) be 5/3?
In Exercises at the indicated point find(a) The slope of the curve,(b) An equation of the tangent, and(c) An equation of the normal.(d) Then draw a graph of the curve, tangent line, and normal line
In Exercises write the fraction in reduced form. 2x² - x 2x²+x-1
In Exercises find the limit and confirm your answer using the Sandwich Theorem. lim 1118 -x 1 - cos x
In Exercises determine the limit by substitution. Support graphically. lim y² + 5y + 6 y+2
In Exercises find the limits. lim int (2x-1) X-7/2
In Exercises use the function ∫ defined and graphed below to answer the questions.(a) Does ∫ (-1) exist?(b) Does limx→ -1+ ∫(x) exist?(c) Does limx→ -1+ ∫(x) = ∫(-1)?(d) Is ∫
In Exercises at the indicated point find(a) The slope of the curve,(b) An equation of the tangent, and(c) An equation of the normal.(d) Then draw a graph of the curve, tangent line, and normal line
In Exercises determine the limit by substitution. Support graphically. lim y--3 y² + 4y + 3 -3
In Exercises find the limit and confirm your answer using the Sandwich Theorem. . lim P1T4 sin x X
In Exercises use the function ∫ defined and graphed below to answer the questions.(a) Does ∫(1) exist?(b) Does limx→1 ∫(x) exist?(c) Does limx→1 ∫(x) = ∫(1)?(d) Is ∫ continuous
In Exercises find the limits. lim int (2x-1) X-7/2
In Exercises at the indicated point find(a) The slope of the curve,(b) An equation of the tangent, and(c) An equation of the normal.(d) Then draw a graph of the curve, tangent line, and normal line
In Exercises find the limit and confirm your answer using the Sandwich Theorem. lim x-xx sin (x²)
In Exercises determine the limit by substitution. Support graphically. lim int x 1-1/2
In Exercises find the limits. lim e cos x X 199
In Exercises use graphs and tables to find the limits. 1 lim x-2x-2
In Exercises use the function ∫ defined and graphed below to answer the questions.(a) Is ∫ defined at x = 2? (Look at the definition of ∫.)(b) Is ∫ continuous at x = 2? x² - 1, 2x, -2x +
In Exercises find the slope of the curve at the indicated point. ∫(x) = |X| at (a) x = 2 (b) x = - 3
In Exercises determine the limit by substitution. Support graphically. lim, (x-6) 2/3
In Exercises find the limits. lim 3- x + sin x x+cos x
In Exercises use the function ∫ defined and graphed below to answer the questions.At what values of x is ∫ continuous? x² - 1, 2x, -2x + 4, 0, y=f(x) f(x) = 1, y=x²-1 y=2x 0 -1≤x≤0 0
In Exercises use graphs and tables to find the limits. X lim X-2 X-2
In Exercises explain why you cannot use substitution to determine the limit. Find the limit if it exists. lim Vx-2 X -2
In Exercises determine whether the limit exists on the basis of the graph of y = ∫(x). The domain of ∫ is the set of real numbers. P per - lim f(x)
In Exercises use the function ∫ defined and graphed below to answer the questions.What value should be assigned to ∫(2) to make the extended function continuous at x = 2? x² - 1, 2x, -2x +
In Exercises use graphs and tables to find the limits. 1 lim x+3x+3
In Exercises find the slope of the curve at the indicated point.∫(x) = |x - 2| at x = 1
In Exercises draw the graph and determine the domain and range of the function.y = log3 (x - 4)
In Exercises find(a) (∫ o g) (-1) (b) (g o ∫) (2) (c) (∫ o ∫) (x) (d) (g o g) (x) f(x) = 2x, g(x)=√x + 1
Which of the following describes the graph of the parametric curve x = 3t, y = 2t, t ≥ 1?(A) Circle (B) Parabola (C) Line segment(D) Line (E) Ray
In Exercises evaluate the expression sin-1(15)) 13 tan sin
By measuring slopes in the figure below, find the temperature change in degrees per inch for the following materials.(a) Gypsum wallboard(b) Fiberglass insulation(c) Wood sheathing(d) Which of the
In Exercises write a piecewise formula for the function. 2 0 2 4
True or False If 43 = 2a, then a = 6. Justify your answer.
In Exercises draw the graph and determine the domain and range of the function.y = log2 (x + 1)
Which of the following describes the graph of the parametric curve x = - 3 sin t, y = - 3 cos t?(A) Circle (B) Parabola (C) Ellipse(D) Hyperbola (E) Line
In Exercises find(a) (∫ o g) (-1) (b) (g o ∫) (2) (c) (∫ o ∫) (x) (d) (g o g) (x) f(x) = — g(x) = 1 Vx+2
In Exercises evaluate the expression in (cos (77)) 11
In Exercises write a piecewise formula for the function. y 이 (1, 1) 2 X
For what value of k are the two lines 2x + ky = 3 and x + y - 1 (a) Parallel?(b) Perpendicular?
In Exercises draw the graph and determine the domain and range of the function.y = - 3 log (x + 2) + 1
In Exercises use the parametric curve x = 5t, y = 3 - 3t, 0 ≤ t ≤ 1.Which of the following is the initial point of the curve?(A) (-5, 6) (B) (0, -3) (C) (0, 3) (D) (5, 0)(E) (10,
True or False The number 3-2 is negative. Justify your answer.
In Exercises write a piecewise formula for the function. 5 (2,5)
In Exercises use the given information to find the values of the six trigonometric functions at the angle θ. Give exact answers.The point P(- 2, 2) is on the terminal side of θ.
a. Explain why c and d are the x-intercept and y-intercept, respectively, of the lineb. How are the x-intercept and y-intercept related to c and d in the line + d 11 2?
Table 1.12 gives the population of California for several years.(a) Let x = 0 represent 1980, x = I represent 1981, and so forth. Find an exponential regression for the data, and superimpose its
In Exercises draw the graph and determine the domain and range of the function.y = 2 In (3 - x) - 4
In Exercises use the parametric curve x = 5t, y = 3 - 3t, 0 ≤ t ≤ 1.Which of the following describes its graph?(A) Circle (B) Parabola (C) Ellipse(D) Line segment (E) Line
In Exercises write a piecewise formula for the function. 2 X
Table 1.11 gives the population of Texas for several years.(a) Let x = 0 represent 1980, x = 1 represent 1981, and so forth. Find an exponential regression for the data, and superimpose its graph on
In Exercises use the given information to find the values of the six trigonometric functions at the angle θ. Give exact answers.The point P(-3, 4) is on the terminal side of θ.
In Exercises use the given information to find the values of the six trigonometric functions at the angle θ. Give exact answers. 0 = tan slu 12,
In Exercises solve for y.In (y - 1) - In2 = x + In x
True or False The parametric curve x = 2 cos (-t), y = 2 sin (-t), 0 ≤ t ≤ 2π is traced clockwise. Justify your answer.
In Exercises find the value of x or y for which the line through A and B has the given slope m.A(-8, -2), B(x, 2), m =2
In Exercises solve for y.In y = 2t + 4
In Exercises use the given information to find the values of the six trigonometric functions at the angle θ. Give exact answers. 0 # = sin-1 8 17
True or False The graph of the parametric curve x = 3 cos t, y = 4 sin t is a circle. Justify your answer.
In Exercises find the value of x or y for which the line through A and B has the given slope m.A (-2, 3), B(4, y), m = -2 /3
In Exercises use the vertical line test (see Exercise 35) to determine whether the curve is the graph of a function.
Find parametrizations to model the motion of a particle that starts at (-a, 0) and traces the ellipseAs indicated.(a) Once clockwise b) Once counterclockwise(c) Twice clockwise (d) Twice

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