Questions and Answers of Calculus Graphical, Numerical, Algebraic

In Exercises use the vertical line test to determine whether the curve is the graph of a function.
In Exercises use the vertical line test to determine whether the curve is the graph of a function. >X
In Exercises match the function with the graph of its end behavior model. y = 2₁4x³+x²-1 X 2-x
In Exercises (a) find a power function end behavior model for ∫. (b) Identify any horizontal asymptotes. f(x) = -4x³+x² - 2x - 1
In Exercises use the graph of the function with domain - 1 ≤ x ≤ 3.Determine(a)(b) g(3).(c) Whether g(x) is continuous at x = 3.(d) The points of discontinuity of g(x).(e) Whether any points of
In Exercises find limx→∞ y and limx→ -∞ y. y 2x + sin x X
In Exercises determine the limit graphically. Confirm algebraically. sin x lim x-0 2x²-x
At t sec after lift-off, the height of a rocket is 3t2 ft. How fast is the rocket climbing after 10 sec?
In Exercises give a formula for the extended function that is continuous at the indicated point. f(x)= x²-9 x + 3 x=-3
In Exercises determine the limit graphically. Confirm algebraically. lim X-0 x + sin x X
In Exercises find limx→∞ y and limx→ -∞ y. sin x 2x² + x
In Exercises give a formula for the extended function that is continuous at the indicated point. f(x) = 12-1 x-17 x=1
In Exercises use the graph of the function with domain - 1 ≤ x ≤ 3.Determine(a)(b)(c) κ(1).(d) Whether k(x) is continuous at x = 1.(e) The points of discontinuity of k(x).(f) Whether any points
What is the rate of change of the area of a circle with respect to the radius when the radius is r = 3 in.?
In Exercises give a formula for the extended function that is continuous at the indicated point. f(x) sin x X x=0
In Exercises (a) find the vertical asymptotes of the graph of ∫(x). (b) Describe the behavior of ∫(x) to the left and right of each vertical asymptote. f(x) = 2-1 2x + 4
In Exercises (a) find the vertical asymptotes of the graph of y = ∫(x), and (b) describe the behavior of ∫(x) to the left and right of any vertical asymptote. f(x) x + 3 x + 2
In Exercises find limx→∞ y and limx→ -∞ y. y x sin x + 2 sin x 2x²
In Exercises (a) find the vertical asymptotes of the graph of ∫(x). (b) Describe the behavior of ∫(x) to the left and right of each vertical asymptote. f(x)= = 1 x²-4
In Exercises determine the limit graphically. Confirm algebraically. lim x-0 sin² x X
The equation for free fall at the surface of Mars is s = 1.86t2 m with t in seconds. Assume a rock is dropped from the top of a 200-m cliff. Find the speed of the rock at t = 1 sec.
What is the rate of change of the volume of a sphere with respect to the radius when the radius is r = 2 in.?
In Exercises determine the limit graphically. Confirm algebraically. lim 0 3 sin 4x sin 3x
In Exercises give a formula for the extended function that is continuous at the indicated point. f(x) sin 4x x = 0
In Exercises (a) find the vertical asymptotes of the graph of y = ∫(x), and (b) describe the behavior of ∫(x) to the left and right of any vertical asymptote. f(x) = * - 1 x²(x + 2)
The equation for free fall at the surface of Jupiter is s = 11.44t2m with t in seconds. Assume a rock is dropped from the top of a 500-m cliff. Find the speed of the rock at t = 2 sec.
In Exercises (a) find the vertical asymptotes of the graph of ∫(x). (b) Describe the behavior of ∫(x) to the left and right of each vertical asymptote. f(x) x² - 2x x + 1
In Exercises use a graph to show that the limit does not exist. ²-4 lim x-x-1 X
In Exercises answer the questions for the piecewise defined function.(a) Find the right-hand and left-hand limits of ∫ at x = - 1, 0, and 1.(b) Does ∫ have a limit as x approaches -1? 0? 1? If
In Exercises give a formula for the extended function that is continuous at the indicated point. f(x) = X -4 √x-2 x = 4
In Exercises (a) find the vertical asymptotes of the graph of ∫(x). (b) Describe the behavior of ∫(x) to the left and right of each vertical asymptote. f(x) = 1-X 2x²5x-3
At what point is the tangent to ∫(x) = x2 + 4x - 1 horizontal?
In Exercises use a graph to show that the limit does not exist. ܕ ܐ ܀ +1 2²-4 lim
In Exercises answer the questions for the piecewise defined function.(a) Find the right-hand and left-hand limits of ∫ at x = 1.(b) Does ∫ have a limit as x→1? If so, what is it? If not, why
In Exercises give a formula for the extended function that is continuous at the indicated point. f(x) x34x² 11x + 30 x²-4 x=2
In Exercises (a) find the vertical asymptotes of the graph of ∫(x). (b) Describe the behavior of ∫(x) to the left and right of each vertical asymptote. f(x) = col x
At what point is the tangent to ∫(x) = 3 - 4x - x2 horizontal?
In Exercises determine the limit. lim int x X-0¹
In Exercises find all points of discontinuity of the function. x+1 4-x²
In Exercises explain why the given function is continuous. - f(x) = x-3
In Exercises determine the limit. Assume that lim f(x) = 0 and lim g(x) = 3. X-4 4 (a) lim (g(x) + 3) (b) lim xf(x) X-4 I-4 (c) lim g²(x) (d) lim g(x) 4 f(x) -1
Find the limits of ∫, g, and ∫g as x→c.(a)(b)(c)(d)(e) Suppose that limx→c ∫(x) = 0 and limx→c g(x) = ∞. Based on your observations in parts (a)-(d), what can you say about
In Exercises (a) find the vertical asymptotes of the graph of ∫(x). (b) Describe the behavior of ∫(x) to the left and right of each vertical asymptote. f(x) = sec x
(a) Find an equation for each tangent to the curve y = 1/(x - 1) that has slope - 1.(See Exercise 21.)(b) Find an equation for each normal to the curve y = 1/(x - 1) that has slope 1.
In Exercises find all points of discontinuity of the function. - g(x) = √3x + 2
In Exercises determine the limit. lim int x
In Exercises explain why the given function is continuous. g(x) = 1 Vr-1
In Exercises (a) find the vertical asymptotes of the graph of ∫(x). (b) Describe the behavior of ∫(x) to the left and right of each vertical asymptote. f(x): || tan x sin x
Find the equations of all lines tangent to y = 9 - x2 that pass through the point (1, 12).
In Exercises determine the limit. lim int x X-0.01
In Exercises use Theorem 7 to show that the given function is continuous. f(x) = X Vx+1
In Exercises find (a) a power function end behavior model and (b) any horizontal asymptotes. f(x) = 2x + 1 x² - 2x + 1
Table gives the amount of federal spending in billions of dollars for national defense for several years.(a) Find the average rate of change in spending from 1990 to 1995.(b) Find the average rate of
In Exercises (a) find the vertical asymptotes of the graph of ∫(x). (b) Describe the behavior of ∫(x) to the left and right of each vertical asymptote. f(x) = col x COS X
In Exercises determine the limit. lim int x .
In Exercises find (a) a power function end behavior model and (b) any horizontal asymptotes. f(x) = 2x² + 5x1 x² + 2x
In Exercises use Theorem 7 to show that the given function is continuous. f(x) = sin (x² + 1)
Table 2.3 gives the amount of federal spending in billions of dollars for agriculture for several years.(a) Let x = 0 represent 1990, x = 1 represent 1991, and so forth. Make a scatter plot of the
In Exercises match the function with the graph of its end behavior model. y = 2x³ 3x² + 1 x + 3
In Exercises find (a) a power function end behavior model and (b) any horizontal asymptotes. f(x) x3 4x² + 3x + 3 x-3
In Exercises determine the limit. lim 3-0 +0 X
In Exercises use Theorem 7 to show that the given function is continuous. f(x) = cos (VI-X)
In Exercises match the function with the graph of its end behavior model. y x¹ + x + 1 2x²+x-3
In Exercises determine the limit. lim -0-x X
True or False If the graph of a function has a tangent line at x = a, then the graph also has a normal line at x = a. Justify your answer.
In Exercises find (a) a power function end behavior model and (b) any horizontal asymptotes. f(x)= x43x²+x-1 3-x+1
In Exercises use Theorem 7 to show that the given function is continuous. f(x) = tan I x²+4
In Exercises which of the statements are true about the function y = ∫(x) graphed there, and which are false? 0 (a) lim f(x) = 1 (c) lim_ f(x) = 1 (e) lim f(x) exists x-0 (g) lim f(x) = 1 1-01 (i)
True or False The graph of ∫(x) =|x| has a tangent line at x = 0. Justify your answer.
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= 1 Vx+2
In Exercises find (a) a right end behavior model and (b) a left end behavior model for the function.∫(x) = x + ex
If the line L tangent to the graph of a function ∫ at the point (2, 5) passes through the point (- 1, - 3), what is the slope of L?(A) - 3/8 (B) 3/8 (C) - 8/3 (D) 8/3 (E)
In Exercises match the function with the graph of its end behavior model. y= 3x3 1-x² 1
In Exercises which of the statements are true about the function y = ∫(x) graphed there, and which are false? 2 f(x) = 1 y = f(x) : 2 X 3 (b) lim f(x) does not exist. (d) lim f(x) = 2 (f) lim f(x)
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 + √4-x
In Exercises find (a) a right end behavior model and (b) a left end behavior model for the function.∫(x) = In |x| + sin x
In Exercises (a) find a power function end behavior model for ∫. (b) Identify any horizontal asymptotes. f(x)=3x²2x + 1
In Exercises use the graph to estimate the limits and value of the function, or explain why the limits do not exist. y o • 3 برا y=f(x) X (a) lim f(x) (b) lim f(x) (c) lim f(x) 1-3 (d) f(3)
Find the average rate of change of ∫(x) = x2 + x over the interval [1, 3],(A) - 5 (B) 1/5 (C) 1/4 (D) 4 (E) 5
In Exercises what value should be assigned to k to make/a continuous function? - f(x) = [x² + 2x 15 x-3 k, x #3 x = 3
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 - 4x|
In Exercises use the graph to estimate the limits and value of the function, or explain why the limits do not exist. y₁ y = g(1) Mam (a) lim_g(r) 1--4 (b) lim g(t) (c) lim g(t) 1-4 (d) g(-4)
Which of the following is an equation of the tangent to the graph of ∫(x) = 2/x at x = 1?(A) y = - 2x (B) y = 2x (C) y = - 2x + 4(D) y = - x + 3 (E) y = x + 3
In Exercises (a) find a power function end behavior model for ∫. (b) Identify any horizontal asymptotes. f(x) 3x²-x+ 5 x²-4
In Exercises use the graph to estimate the limits and value of the function, or explain why the limits do not exist. y A -2 y=p(s) 8 (a) lim_p(s) (b) limp(s) 3--2+ (c) limp(s) 3--2 (d) p(-2)
In Exercise sketch a graph of a function ∫ that satisfies the given conditions. lim f(x) does not exist, lim f(x) = f(2)= 3 3-2 X-2
In Exercises sketch a possible graph for a function ∫ that has the stated properties.∫(- 2) exists, limX→ -2+ ∫(x) = ∫(- 2), but limX→ -2 ∫(x) does not exist.
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
In Exercises (a) find a power function end behavior model for ∫. (b) Identify any horizontal asymptotes. f(x) = 4x³2x+1 x-2
In Exercises use the graph to estimate the limits and value of the function, or explain why the limits do not exist. yt y=F(x) H (a) lim F(x) (b) lim F(x) x-0+ (c) lim F(x) X-0 (d) F(0)
In Exercises the curve y = ∫(x) has a vertical tangent at x = a ifIn each case, the right- and left-hand limits are required to be the same: both + ∞ or both - ∞. Use graphs to investigate
Find the average rate of change of ∫(x) = 1 + sin x over the interval [0, π/2].
In Exercises sketch a possible graph for a function ∫ that has the stated properties.∫(4) exists, limX→ 4 ∫(x) exists, but ∫ is not continuous at x = 4.
In Exercises (a) find a power function end behavior model for ∫. (b) Identify any horizontal asymptotes. f(x)= = -x+ + 2x² + x - 3 x² - 4 X
In Exercises use the graph to estimate the limits and value of the function, or explain why the limits do not exist. y₁ y = G(x) el 2 X (a) lim G(x) (b) lim G(x) (c) lim G(x) x-2 (d) G(2)
Find the instantaneous rate of change of the volume V = (1/3)πr2H of a cone with respect to the radius r at r = a if the height H does not change.
In Exercises sketch a possible graph for a function that has the stated properties.∫(x) is continuous for all x except x = 1, where ∫ has a nonremovable discontinuity.
In Exercises the curve y = ∫(x) has a vertical tangent at x = a ifIn each case, the right- and left-hand limits are required to be the same: both + ∞ or both - ∞. Use graphs to investigate
In Exercises find (a) a simple basic function as a right end behavior model and (b) a simple basic function as a left end behavior model for the function.y = ex - 2x
In Exercises match the function with the table. Y₁ x²+x-2 x-1

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