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mathematics
calculus graphical, numerical, algebraic

Calculus Graphical, Numerical, Algebraic 3rd Edition Ross L. Finney, Franklin D. Demana, Bert K. Waits, Daniel Kennedy - Solutions

Valuepark charge $1.10 per hour or fraction of an hour for airport parking. The maximum charge per day is $7.25.(a) Write a formula that gives the charge for x hours with 0 ≤ x ≤ 24. (b) Graph the function in part (a). At what values of x is it continuous?
In Exercises complete parts (a), (b), and (c) for the piecewise defined function.(a) Draw the graph of ∫.(b) Determine limx→c+ ∫(x) and limx→c- ∫(x).(c) Does limx→c ∫(x ) exist? If so, what is it? If not, explain. - x², x=-1 x = -1 c = -1, f(x) = = 12₂.²
In Exercises find the limit of ∫(x) as (a) x→ - ∞, (b) x→∞, (c) x→0-, and (d) x→0+. x-2 f(x)=x-1' 1/x². x≤0 x>0
True or False A continuous function cannot have a point of discontinuity. Justify your answer.
In Exercises complete parts (a)-(d) for the piecewise-defined function.(a) Draw the graph off.(b) At what points c in the domain of ∫ does limx→c ∫(x) exist?(c) At what points c does only the left-hand limit exist?(d) At what points c does only the right-hand limit exist? f(x) = sin
In Exercises complete parts (a)-(d) for the piecewise-defined function.(a) Draw the graph off.(b) At what points c in the domain of ∫ does limx→c ∫(x) exist?(c) At what points c does only the left-hand limit exist?(d) At what points c does only the right-hand limit exist? f(x) = cos
On which of the following intervals is(A) (0, ∞)(B) [0, ∞)(C) (0, 2)(E) [l, ∞)(D) (l, 2) f(x)= not continuous?
In Exercises complete parts (a)-(d) for the piecewise-defined function.(a) Draw the graph off.(b) At what points c in the domain of ∫ does limx→c ∫(x) exist?(c) At what points c does only the left-hand limit exist?(d) At what points c does only the right-hand limit exist? VI-x², f(x) =
Which of the following points is not a point of discontinuity of ????(x) = √x - 1?(A) x = - 1 (B) x = -1/2 (C) x = 0(D) x = 1/2 (E) x = 1
Suppose that g1(x) is a right end behavior model for ∫1(x) and that g2(x) is a right end behavior model for ∫2(x). Explain why this makes g1(x)/g2(x) a right end behavior model for ∫1(x)/∫2(x).
In Exercises complete parts (a)-(d) for the piecewise-defined function.(a) Draw the graph off.(b) At what points c in the domain of ∫ does limx→c ∫(x) exist?(c) At what points c does only the left-hand limit exist?(d) At what points c does only the right-hand limit exist? [x, f(x)= 1, 1
Which of the following statements about the functionis not true?(A) ∫(1) does not exist.(B) limx→0+ ∫(X) exists.(C) limx→2- ∫(x) exists.(D) limx→1 ∫(x) exists.(E) limx→1 ∫(x) ≠ ∫(1) 2.x, f(x) = 1. -x +3. 0
Let L be a real number, limx→c ∫(x) = L, and limx→c g(x) = ∞ or - ∞. Can limx→c (∫(x) + g(x)) be determined? Explain.
In Exercises find the limit graphically. Use the Sandwich Theorem to confirm your answer. lim x sin x
In Exercises what value should be assigned to k to make/a continuous function? sin x 2.x |k, x 0 x=0
In Exercises verify that the function is continuous and state its domain. Indicate which theorems you are using, and which functions you are assuming to be continuous. y = x²-1 x-1 2, x 1 x = 1
Which of the following is an equation of the normal to the graph of ∫(x) = 2/x at x = 1 ? +2 (By = 글 (Ox = 2+2 y (A) y = 글+2 (D) y = 글 +2 (E) y = 2x + 5
In Exercises (a) find a power function end behavior model for ∫. (b) Identify any horizontal asymptotes. f(x) = x-2 2x² + 3x - 5
In Exercises use the graph to estimate the limits and value of the function, or explain why the limits do not exist. y↑ 2 N y=f(h) h (a) lim f(h) (b) lim f(h) 4-0 (c) lim f(h) h→0 (d) f(0)
In Exercise sketch a graph of a function ∫ that satisfies the given conditions. lim f(x) 3. lim f(x) = ∞, x--∞" lim f(x) = co, lim f(x) = -
In Exercises complete the following for the function,(a) Compute the difference quotient(b) Use graphs and tables to estimate the limit of the difference quotient in part (a) as h→0.(c) Compare your estimate in part (b) with the given number.(d) Based on your computations, do you think the graph
In Exercises sketch a possible graph for a function ∫ that has the stated properties.∫(3) exists but limX→3, ∫(x) does not.
In Exercises find the increments Δx and Δy from point A to point B.A (-5, 2) B (3, 5)
In Exercises find the points of continuity and the points of discontinuity of the function. Identify each type of discontinuity. y= V2r-1 2x
In Exercises find the quotient q(x) and remainder r(x) when ∫(x) is divided by g(x).∫(x) = 2x5 - x3 + x - 1, g(x) = x3 - x2 + 1
In Exercises write an equation for the specified line.Through (1, 6) and (4, -1)
In Exercises find the average rate of change of the function over each interval.∫(x) = 2 + cos t(a) [0, π] (b) [- π , π]
In Exercises use graphs and tables to find (a) limx→∞ ∫(x) and (b) limx→ -∞ ∫(x) (c) Identify all horizontal asymptotes. f(x)= 2x - 1 |x|-3
In Exercises use limx→c k = k, limx→c x = c, and the properties of limits to find the limit. lim x-x²¹+1 x² +9
In Exercises write the inequality in the form a < x < b|x| < c2
In Exercises find the limits. - lim 1110 x4+x³ 12x³ + 128
Use factoring to solve 2x2 + 9x - 5 = 0.
In Exercises find the points of continuity and the points of discontinuity of the function. Identify each type of discontinuity.y = |x|/x
In Exercises use graphs and tables to find (a) limx→∞ ∫(x) and (b) limx→ -∞ ∫(x) (c) Identify all horizontal asymptotes. f(x) = X
In Exercises write a formula for (a) ∫(- x) and (b) ∫(1/x). Simplify where possible.∫(x) = COS X
In Exercises write the inequality in the form a < x < b|x - 2| < 3
In Exercises find the limits. lim 0 sin 2x 4x
In Exercises determine the limit by substitution. Support graphically. lim 3x²(2x - 1) -1/2
Let y = sin (ax) + cos (ax).Use the symbolic manipulator of a computer algebra system (CAS) to help you with the following:(a) Express y as a sinusoid for a = 2,3, 4, and 5.(b) Conjecture another formula for y for a equal to any positive integer n.(c) Check your conjecture with a CAS.(d) Use the
This activity investigates how to find the distance from a point P{a, b) to a line L: Ax + By = C.(a) Write an equation for the line M through P perpendicular to L.(b) Find the coordinates of the point Q in which M and L intersect.(c) Find the distance from P to Q.
Let ∫(x) = 1 - 3 cos (2x).(a) What is the domain o f ∫? (b) What is the range o f ∫?(c) What is the period o f ∫?(d) Is ∫ an even function, odd function, or neither?(e) Find all the zeros of ∫ in π/2 ≤ x ≤ π.
In Exercises a portion of the graph of a function defined on [-2, 2] is shown. Complete each graph assuming that the graph is (a) even, (b) odd. -2 y 1.31 0 -1.3- X
In Exercises find the limits. lim (x³2x2 + 1) 3--2
In Exercises find the points of continuity and the points of discontinuity of the function. Identify each type of discontinuity. 1 y = (x + 2)²
In Exercises find ∫-1 and graph ∫, ∫-, and y = x in the same square viewing window.∫(x) = 2x - 3
Use graphing to solve x3 + 2x - 1 = 0.
In Exercises find the points of continuity and the points of discontinuity of the function. Identify each type of discontinuity.y = cot x
In Exercises write a formula for (a) ∫(- x) and (b) ∫(1/x). Simplify where possible.∫(x) = e-x
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. lim f(x) X-C
In Exercises use the function ∫ defined and graphed below to answer the questions.What new value should be assigned to ∫(1) to make the new function continuous at x = 1 ? 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-3x + 3 X
In Exercises determine whether the curve has a tangent at the indicated point. If it does, give its slope. If not, explain why not. f(x) -X, x < 0 lx²-x, x ≥ 0 = {₁²₁² at x = 0
In Exercises explain why you cannot use substitution to determine the limit. Find the limit if it exists. lim X-0 X
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. lim f(x) X-C
In Exercises use the function ∫ defined and graphed below to answer the questions.Is it possible to extend ∫ to be continuous at x = 0? If so, what value should the extended function have there? If not, why not? x² - 1, 2x, -2x + 4, 0, y=f(x) f(x) = 1, y=x²-1 y=2x 0 -1≤x≤0 0
In Exercises determine whether the curve has a tangent at the indicated point. If it does, give its slope. If not, explain why not. (1/x. f(x)=4-x 4 x≤2 x>2 at x = 2
In Exercises find ∫-1 and graph ∫, ∫-, and y = x in the same square viewing window.∫(x) = ex
In Exercises find the average rate of change of the function over each interval.(a) [0, 2] (b) [10, 12] f(x)=√4x + 1
In Exercises find the increments Δx and Δy from point A to point B.A (l, 3) B (a, b)
In Exercises use graphs and tables to find (a) limx→∞ ∫(x) and (b) limx→ -∞ ∫(x) (c) Identify all horizontal asymptotes. f(x) = sin 2x X
In Exercises find ∫(2). f(x)= 4x²-5 x³ + 4
In Exercises an object dropped from rest from the top of a tall building falls y = 16t2 feet in the first t seconds.Find the average speed during the first 4 seconds of fall.
Find(A) 5/3 (B) 13/3 (C) 7 (D) ∞ (E) Does not exist lim f(x), if it exists, where
Which of the following is an equation for the tangent line to ∫(x) = 9 - x2 at x = 2? (A) y = x + 9 2 (C) y = -4x-3 (E) y = 4x + 13 (B) y = -4x + 13 (D) y = 4x - 3
In Exercises use graphs and tables to find (a) limx→∞ ∫(x) and (b) limx→ -∞ ∫(x) (c) Identify all horizontal asymptotes. f(x) = cos X
In Exercises find the average rate of change of the function over each interval.∫(x) = x3 + 1(a) [2, 3] (b) [-1, 1]
In Exercises find ∫(2). f(x) = 2x³5x² + 4
In Exercises an object dropped from rest from the top of a tall building falls y = 16t2 feet in the first t seconds.Find the average speed during the first 3 seconds of fall.
Find(A) -1 (B) 1 (C) 2 (D) 5 (E) Does not exist x²-x-6 lim x-3 x-3 if it exists.
Which of the following statements is false for the function(A) limx→4 ∫(x) exists (B) ∫(4) exists(C) limx→6 ∫(x) exists (D) limx→8- ∫(x) exists(E) ∫ is continuous at x = 4 4 f(x) = 2, -x+7, 1, 0≤x≤4 x = 4 4< x≤6 6
In Exercises find the limits. x² + 1 lim x-2 3x² - 2x + 5
Let ∫(x) = int x. Find each limit (a) lim f(x) (b) lim f(x) (c) lim f(x) (d) f(-1)
In Exercises find the points of continuity and the points of discontinuity of the function. Identify each type of discontinuity. x + 1 y= x² - 4x +3 2
In Exercises find the limits. làm V1 – 2x - 3-4
In Exercises find the points of continuity and the points of discontinuity of the function. Identify each type of discontinuity. - y = 1 x² + 1
In Exercises find ∫-1 and graph ∫, ∫-, and y = x in the same square viewing window.∫(x) = tan-1 x
In Exercises find the slope of the line determined by the points.(- 2 ,3), (5, - 1)
In Exercises find the average rate of change of the function over each interval.∫(x) = ex(a) [- 2, 0] (b) [1, 3]
In Exercises use graphs and tables to find (a) limx→∞ ∫(x) and (b) limx→ -∞ ∫(x) (c) Identify all horizontal asymptotes. - f(x) = e X
In Exercises find ∫(2). f(x) = sin 7- 2
In Exercises an object dropped from rest from the top of a tall building falls y = 16t2 feet in the first t seconds.Find the speed of the object at t = 3 seconds and confirm your answer algebraically.
(a) Find the domain and range o f ∫(b) Is ∫ even, odd, or neither? Justify your answer.(c) Find limx→∞ ∫ (x).(d) Use the Sandwich Theorem to justify your answer to part (c). Let f(x) = COS X X
Let ∫(x) = 2x - x2.(a) Find ∫(3). (b) Find ∫(3 + h).(d) Find the instantaneous rate of change of ∫ at x = 3. (e) Find f(3+h)-f(3) h
In Exercises find the points of continuity and the points of discontinuity of the function. Identify each type of discontinuity.y = |x - 1|
In Exercises find ∫-1 and graph ∫, ∫-, and y = x in the same square viewing window.∫(x) = cot-1 x
In Exercises a distance-time graph is shown.(a) Estimate the slopes of the secants PQ1, PQ2, PQ3, and PQ4, arranging them in order in a table. What is the appropriate unit for these slopes?(b) Estimate the speed at point P.The accompanying figure shows a distance-time graph for a wrench that
In Exercises use graphs and tables to find (a) limx→∞ ∫(x) and (b) limx→ -∞ ∫(x) (c) Identify all horizontal asymptotes. f(x)= |x| |x + 1
In Exercises determine the limit by substitution. Support graphically. lim (x + 3)1998 4-4
In Exercises write the inequality in the form a < x < b|x - c| < d2
In Exercises find the limits. lim x csc x + 1 X CSC X
In Exercises letSolve the equation ∫(x) = 4. f(x) = (5-x. x≤3 1-x² + 6x8, x> 3.
In Exercises write a formula for (a) ∫(- x) and (b) ∫(1/x). Simplify where possible. f(x) = In x X
In Exercises find the points of continuity and the points of discontinuity of the function. Identify each type of discontinuity.y = e1/x
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 the same square viewing window. y = x² at x = -2
In Exercises write an equation for the specified line.Through (- 1, 3) and parallel to 2x + 3y = 5
In Exercises find the limit and confirm your answer using the Sandwich Theorem. 1² X 500 - [ lim
In Exercises, write the fraction in reduced form. x3x18 x + 3
In Exercises determine the limit by substitution. Support graphically. lim (x³ + 3x²2r-17)
In Exercises determine the limit by substitution. Support graphically. lim √x + 3
In Exercises determine whether the curve has a tangent at the indicated point. If it does, give its slope. If not, explain why not. f(x) [22x-x², 2x + 2, x

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