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mathematics
calculus early transcendentals 9th

Questions and Answers of Calculus Early Transcendentals 9th

Determine whether the sequence is convergent or divergent. If it is convergent, find its limit. an 2 + n3 1 + 2n³ 3
Two similar-looking series are given. Test each one for convergence or divergence.a.b. n-1 (-1)" 73/12
Evaluate the definite integral. ₁x√a²-x² dx
Suppose h is a function such that h(1) = –2, h'(1) = 2, h"(1) = 3, h(2) = 6, h'(2) = 5, h"(2) = 13, and h" is continuous everywhere. Evaluate ∫21 h"(u) du.
Match the polar equations with the graphs labeled I–VI. Give reasons for your answer. * III II У IV VI --------- 3
Write a polar equation of a conic with the focus at the origin and the given data.Ellipse, eccentricity 1/3, directrix y = 6
Two similar-looking series are given. Test each one for convergence or divergence.a.b. 8 100 1 ni 5"
Determine whether the statement is true or false. If it is true, explain why. If it is false, explain why or give an example that disproves the statement.If limn→∞ an = 0, then Σan is convergent.
Determine whether the statement is true or false. If it is true, explain why. If it is false, explain why or give an example that disproves the statement.The series Σ∞n=1 n–sin1 is convergent.
Suppose you know that the seriesconverges for |x| < 2. What can you say about the following series? Why? Σ=o bnx" n=0
Test the series for convergence or divergence. 2 - 3 + ² - 3 + 1 - ...
(a) Use the Direct Comparison Test to show that the first series converges by comparing it to the second series.(b) Use the Limit Comparison Test to show that that the first series converges by
Two similar-looking series are given. Test each one for convergence or divergence.a.b. 8 Σ ζ 1-u n 3″
List the first five terms of the sequence.an = n3 − 1
If f(n)(0) = (n + 1)! for n = 0, 1, 2, . . . , find the Maclaurin series for f and its radius of convergence.
Determine whether the statement is true or false. If it is true, explain why. If it is false, explain why or give an example that disproves the statement.If limn→∞ an = L, then limn→∞ a2n+1 =
Find the radius of convergence and interval of convergence of the power series. U I=U n x" 00
Test the series for convergence or divergence. 9 + - +/-% + ½ -
Use the Integral Test to determine whether the series is convergent or divergent. 00 Ση n=1 -3
The graph shows the velocity (in m/s) of an electric autonomous vehicle moving along a straight track. At t = 0 the vehicle is at the charging station.(a) How far is the vehicle from the charging
Which of the integralsandhas the largest value? Why? fỉ arctan x dx, fỉ arctan Vx dx,
The position of an object in circular motion is modeled by the given parametric equations, where t is measured in seconds. How long does it take to complete one revolution? Is the motion clockwise or
Find dx/dt, dy/dt, and dy/dx.x − t 2 ln t, y − t 2 2 t22
Sketch the curve by using the parametric equations to plot points. Indicate with an arrow the direction in which the curve is traced as t increases.x = 2t − t, y = 2−t + t,
The graph of f is shown.(a) Explain why the series 1.1 + 0.7x2 + 2.2x3 + ∙ ∙ ∙ is not the Maclaurin series of f.(b) Explain why the series1.6 − 0.8(x − 1) + 0.4(x − 1)2 − 0.1(x − 1)3
Find parametric equations for the position of a particle moving along a circle as described.The particle travels clockwise around a circle centered at the origin with radius 5 and completes a
Determine whether the sequence is convergent or divergent. If it is convergent, find its limit. an 90+1 10"
(a) What is a convergent sequence?(b) What is a convergent series?(c) What does limn→∞ an = 3 mean?(d) What does Σ∞n=1 an = 3 mean?
(a) What is a sequence?(b) What does it mean to say that limn→∞ an = 8?(c) What does it mean to say that limn→∞ an = ∞ ?
Use the Ratio Test to determine whether the series is convergent or divergent. 8 n=1 n 5"
Find the sum of the serieswhere the terms are the reciprocals of the positive integers whose only prime factors are 2s and 3s. 1 + - 3 - + + 810 12
Test the series for convergence or divergence. (-1)^+1 n=0 √n +1 00
Determine whether the series is convergent or divergent. Σ n=1 n? + 1 2³ +1 n3 3
Test the series for convergence or divergence. 00 1 Σ n=2 n√//ln n
Determine whether the statement is true or false. If it is true, explain why. If it is false, explain why or give an example that disproves the statement.If an> 0 and limn→∞ (an+1/an) < 1, then
Determine whether the series is convergent or divergent by expressing sn as a telescoping sum. If it is convergent, find its sum.123 Σ n=1\n 1 + 2 n
Find the radius of convergence and interval of convergence of the power series. (-1)^ n=2 n ln n 00 x"
Find the radius of convergence and interval of convergence of the power series. Σ n=1 (-1)^-1 n5" -x Μ
(a) Use Equation 1 to find a power series representation for f(x) = ln(1 – x). What is the radius of convergence?(b) Use part (a) to find a power series for f(x) = x ln(1 – x).(c) By putting x =
Determine whether the statement is true or false. If it is true, explain why. If it is false, explain why or give an example that disproves the statement.If an > 0 and Σan converges, then
Determine whether the statement is true or false. If it is true, explain why. If it is false, explain why or give an example that disproves the statement. ху a2f ах ду
Find dz/dt in two ways: by using the Chain Rule, and by first substituting the expressions for x and y to write z as a function of t. Do your answers agree?z = xyey, x = t2,
Test the series for convergence or divergence. 00 n=1 4 - cos n √n
Determine whether the statement is true or false. If it is true, explain why. If it is false, explain why or give an example that disproves the statement.There exists a function f with continuous
Determine whether the series is absolutely convergent, conditionally convergent, or divergent. Σ (−1)". n=1 n νη3 + 2
Find the radius of convergence and interval of convergence of the power series. n2x" Σ H= 2.4.6. . (2n)
Test the series for convergence or divergence. 00 Σ tan(1/n) n=1
Find the radius of convergence and interval of convergence of the power series. Σ -(x - a)",_b > 0 0 b" In n =
Find the sum of the series. 00 Σ n=0 (−1)"π" 32n (2n)!
(a) Find the eccentricity(b) Identify the conic(c) Give an equation of the directrix(d) Sketch the conic. r= 2 3 + 3 sine
Determine whether the statement is true or false. If it is true, explain why. If it is false, explain why or give an example that disproves the statement.The polar curvesr = 1 − sin 2θ
Describe the motion of a particle with position (x, y), where x = 2 + 4 cos πt and y = –3 + 4 sin πt, as t increases from 0 to 4.
Find the vertex, focus, and directrix of the parabola and sketch its graph.y2 + 6y + 2x + 1 = 0
Write a polar equation of a conic with the focus at the origin and the given data.Parabola, vertex (3, π/2)
Determine whether the statement is true or false. If it is true, explain why. If it is false, explain why or give an example that disproves the statement.The equations r = 2, x2 − y2 = 4, and x = 2
Find the vertex, focus, and directrix of the parabola and sketch its graph.2x2 – 16x – 3y + 38 = 0
Find an equation of the parabola. Then find the focus and directrix. -2 1 x
Write a polar equation of a conic with the focus at the origin and the given data.Hyperbola, eccentricity 2, directrix r = –2 sec θ
Determine whether the statement is true or false. If it is true, explain why. If it is false, explain why or give an example that disproves the statement.The parametric equations x = t2, y = t4 have
Match the polar equations with the graphs labeled I–VI. Give reasons for your answer. * III II У IV VI --------- 3
Find an equation of the tangent to the curve at the point corresponding to the given value of the parameter.x = sin 2t + cos t, y = cos 2t − sin t; t = π
Find an equation of the parabola. Then find the focus and directrix. y. 0 -1 2 X
Sketch the region in the plane consisting of points whose polar coordinates satisfy the given conditions.0 ≤ r ≤ 1, −π/2 ≤ θ ≤ π/2
Determine whether the statement is true or false. If it is true, explain why. If it is false, explain why or give an example that disproves the statement.The graph of y2 = 2y + 3x is a parabola.
Find an equation of the tangent to the curve at the point corresponding to the given value of the parameter.x = et sin πt, y = e2t; t = 0
Match the polar equations with the graphs labeled I–VI. Give reasons for your answer. * III II У IV VI --------- 3
Sketch the curve and find the area that it encloses.r = 2 + 2 cos θ
Match the polar equations with the graphs labeled I–VI. Give reasons for your answer. * III II У IV VI --------- 3
Determine whether the statement is true or false. If it is true, explain why. If it is false, explain why or give an example that disproves the statement.A tangent line to a parabola intersects the
Find the vertices and foci of the ellipse and sketch its graph. x 4 + y² 3 1
Determine whether the statement is true or false. If it is true, explain why. If it is false, explain why or give an example that disproves the statement.A hyperbola never intersects its directrix.
Sketch the curve and find the area that it encloses.r = 2 sin 3θ
Match the polar equations with the graphs labeled I–VI. Give reasons for your answer. * III II У IV VI --------- 3
Sketch the polar curve.r = sin 4θ
Find the vertices and foci of the ellipse and sketch its graph.x2 + 3y2 = 9
Match the polar equations with the graphs labeled I–VI. Give reasons for your answer. * III II У IV VI --------- 3
Find the vertices and foci of the ellipse and sketch its graph.x2 = 4 – 2y2
(a) Find the eccentricity(b) Identify the conic(c) Give an equation of the directrix(d) Sketch the conic. r= 4 5-4 sine
Sketch the polar curve.r = 1 + cos 2θ
Find the vertices and foci of the ellipse and sketch its graph.4x2 + 25y2 – 50y = 75
(a) Find the eccentricity(b) Identify the conic(c) Give an equation of the directrix(d) Sketch the conic. r = 1 2 + sin 0
Sketch the polar curve.r = 2 cos(θ/2)
Find the vertices and foci of the ellipse and sketch its graph.9x2 – 54x + y2 + 2y + 46 = 0
Sketch the polar curve. 3 1 + 2 sin 0
Find an equation of the ellipse. Then find its foci. у 0 1 x
Sketch the polar curve. 3 2 - 2 cos 0
Find an equation of the ellipse. Then find its foci. 2 x
(a) Find the eccentricity(b) Identify the conic(c) Give an equation of the directrix(d) Sketch the conic. r = 5 2-4 cos 0
(a) Find the eccentricity(b) Identify the conic(c) Give an equation of the directrix(d) Sketch the conic. T 9 6 + 2 cos 0
Find a polar equation for the curve represented by the given Cartesian equation.x + y = 2
(a) Find the eccentricity(b) Identify the conic(c) Give an equation of the directrix(d) Sketch the conic. r = 1 3-3 sin 0
Find the vertices, foci, and asymptotes of the hyperbola and sketch its graph. x² 36 y² 64 = 1
Find a polar equation for the curve represented by the given Cartesian equation.x2 + y2 = 2
(a) Find the eccentricity(b) Identify the conic(c) Give an equation of the directrix(d) Sketch the conic. r 3 4-8 cos 0
The figure shows a graph of r as a function of θ in Cartesian coordinates. Use it to sketch the corresponding polar curve. TA 2 0 -2 7 2π 0
Find the vertices, foci, and asymptotes of the hyperbola and sketch its graph.x2 – y2 = 100
(a) Find the eccentricity(b) Identify the conic(c) Give an equation of the directrix(d) Sketch the conic. 4 2 + 3 cos 0
Find the vertices, foci, and asymptotes of the hyperbola and sketch its graph.y2 – 16x2 = 16
Find a polar equation for the curve represented by the given Cartesian equation.x = −1
Find the slope of the tangent line to the given curve at the point corresponding to the specified value of the parameter.x = ln t, y = 1 + t2; t = 1

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