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mathematics
precalculus

Questions and Answers of Precalculus

Use a graph of the sequence to decide whether the sequence is convergent or divergent. If the sequence is convergent, guess the value of the limit from the graph and then prove your guess. (See the
Use a graph of the sequence to decide whether the sequence is convergent or divergent. If the sequence is convergent, guess the value of the limit from the graph and then prove your guess. (See the
Determine whether the sequence converges or diverges. If it converges, find the limit.
Determine whether the sequence converges or diverges. If it converges, find the limit.
Determine whether the sequence converges or diverges. If it converges, find the limit. S1 1 1 1 1 1 1 1 lI> 3, 2, 4, 3, 5, 4, 6,** } d..
Determine whether the sequence converges or diverges. If it converges, find the limit. {0, 1, 0, 0, 1, 0, 0, 0, 1, . . . }
Determine whether the sequence converges or diverges. If it converges, find the limit. п — Vn + IVn +3 а, — п —
Determine whether the sequence converges or diverges. If it converges, find the limit. an = arctan (ln n)
Determine whether the sequence converges or diverges. If it converges, find the limit. (In n)? an п
Determine whether the sequence converges or diverges. If it converges, find the limit. In(2n? + 1) – lIn(n² + 1)
Determine whether the sequence converges or diverges. If it converges, find the limit. п an
Determine whether the sequence converges or diverges. If it converges, find the limit. п an п
Determine whether the sequence converges or diverges. If it converges, find the limit.
Determine whether the sequence converges or diverges. If it converges, find the limit. an = n sin(1/n)
Determine whether the sequence converges or diverges. If it converges, find the limit. an V2'+3n
Determine whether the sequence converges or diverges. If it converges, find the limit.
Determine whether the sequence converges or diverges. If it converges, find the limit. = In(n + 1) – In n an
Determine whether the sequence converges or diverges. If it converges, find the limit.{n2e-n}
Determine whether the sequence converges or diverges. If it converges, find the limit. -1 tan'n an
Determine whether the sequence converges or diverges. If it converges, find the limit. {sin n}
Determine whether the sequence converges or diverges. If it converges, find the limit. In n In 2n
Determine whether the sequence converges or diverges. If it converges, find the limit. 1)! (2n (2п + 1)!
Determine whether the sequence converges or diverges. If it converges, find the limit.
Determine whether the sequence converges or diverges. If it converges, find the limit.
Determine whether the sequence converges or diverges. If it converges, find the limit. ,2n/(n+2) An
Determine whether the sequence converges or diverges. If it converges, find the limit. п? an Уп3 + 4n
Determine whether the sequence converges or diverges. If it converges, find the limit. пт An cos п+1
Determine whether the sequence converges or diverges. If it converges, find the limit. 1 + 4n? an 1 + n?
Determine whether the sequence converges or diverges. If it converges, find the limit. 4" 1 + 9"
Determine whether the sequence converges or diverges. If it converges, find the limit. а, — е Vп
Determine whether the sequence converges or diverges. If it converges, find the limit. 3. An 'п +2
Determine whether the sequence converges or diverges. If it converges, find the limit.an = 3n7-n
Determine whether the sequence converges or diverges. If it converges, find the limit.an = 2 + (0.86)n
Determine whether the sequence converges or diverges. If it converges, find the limit. п an п3 — 2п
Determine whether the sequence converges or diverges. If it converges, find the limit. 3 + 5n? an п
Calculate, to four decimal places, the first ten terms of the sequence and use them to plot the graph of the sequence by hand. Does the sequence appear to have a limit? If so, calculate it. If not,
Calculate, to four decimal places, the first ten terms of the sequence and use them to plot the graph of the sequence by hand. Does the sequence appear to have a limit? If so, calculate it. If not,
Calculate, to four decimal places, the first ten terms of the sequence and use them to plot the graph of the sequence by hand. Does the sequence appear to have a limit? If so, calculate it. If not,
Find a formula for the general term an of the sequence, assuming that the pattern of the first few terms continues.{1, 0, -1, 0, 1, 0, -1, 0, . . .}
Find a formula for the general term an of the sequence, assuming that the pattern of the first few terms continues.{5, 8, 11, 14, 17, . . .}
Find a formula for the general term an of the sequence, assuming that the pattern of the first few terms continues. |{-3, 2, –3. §. – 4. ..} 4 8 _ 16 16
Find a formula for the general term an of the sequence, assuming that the pattern of the first few terms continues. |{4, –1, , 4,–16 64 .. 4>
Find a formula for the general term an of the sequence, assuming that the pattern of the first few terms continues. 2> 4, 6> 8, 10:
List the first five terms of the sequence. = An An-1 ај 3D 2, а, —D 1, a2 = 1, an+1
List the first five terms of the sequence. ал a¡ = 2, an+1 1 + an
List the first five terms of the sequence. ал 6, An+1 ат п
List the first five terms of the sequence. 5an - 3 ај 3D 1, аn+1
List the first five terms of the sequence.
List the first five terms of the sequence. An (п + 1)!
List the first five terms of the sequence. пт cos an
List the first five terms of the sequence. (–1)"-1 ал 5"
List the first five terms of the sequence. п? — 1 an п? + 1
List the first five terms of the sequence.
Find an equation of the hyperbola with foci (0, ±4) and asymptotes y = ±3x.
Find an equation of the parabola with focus (2, 1) and directrix x = -4.
Find an equation of the ellipse with foci (±4, 0) and vertices (±5, 0).
Find the length of the curve. r = sin'(0/3), 0< 0 < T
Find the length of the curve. T< 0 < 2m r = 1/0,
Find the length of the curve. x = 2 + 3t, y= cosh 3t, 0
Find the area of the region that lies inside the curve r = 2 + cos 2θ but outside the curve r = 2 + sin θ.
Find the points of intersection of the curves r = cot θ and r = 2 cos θ.
Find the area enclosed by the inner loop of the curve r = 1 - 3 sin θ.
Find the area enclosed by the curve in Exercise 29.Exercise 29At what points does the curvehave vertical or horizontal tangents? Use this information to help sketch the curve. x = 2a cos t y = 2a sin
At what points does the curvehave vertical or horizontal tangents? Use this information to help sketch the curve. y = 2a sin t – a sin 2t x = 2a cos t – a cos 2t
Find the area enclosed by the loop of the curve in Exercise 27.Use a graph to estimate the coordinates of the lowest point on the curve x = t3 - 3t, y = t2 + t + 1. Then use calculus to find the
Find dy/dx and d2y/dx2.x = 1 + t2, y = t - t3
Find dy/dx and d2y/dx2.x = t + sin t, y = t - cos t
Sketch the polar curve.r = 3/2 - 2 cos θ
Sketch the polar curve.r = 2 cos(θ/2)
Sketch the polar curve.r = 3 + cos 3θ
Sketch the polar curve.r = cos 3θ
Sketch the polar curve.r = sin 4θ
Sketch the polar curve.r = 1 + sin θ
Sketch the region consisting of points whose polar coordinates satisfy 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
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
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.
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
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
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 r = sin
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 a point is represented by (x, y) in
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 length of the curve
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 x = f (t) and y = g(t) are twice
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 the parametric curve x = f (t), y = g(t)
Comet Hale-Bopp, discovered in 1995, has an elliptical orbit with eccentricity 0.9951. The length of the orbit’s major axis is 356.5 AU. Find a polar equation for the orbit of this comet. How close
The orbit of Halley’s comet, last seen in 1986 and due to return in 2061, is an ellipse with eccentricity 0.97 and one focus at the sun. The length of its major axis is 36.18 AU. [An astronomical
Show that a conic with focus at the origin, eccentricity e, and directrix y = d has polar equation ed 1+ e sine
(a) Find the eccentricity, (b) Identify the conic, (c) Give an equation of the directrix, and (d) Sketch the conic. 3 r = 4 - 8 cos 0
(a) Find the eccentricity, (b) Identify the conic, (c) Give an equation of the directrix, and (d) Sketch the conic. 3 - 3 sine
(a) Find the eccentricity, (b) Identify the conic, (c) Give an equation of the directrix, and (d) Sketch the conic. 2 - 4 cos e
(a) Find the eccentricity, (b) Identify the conic, (c) Give an equation of the directrix, and (d) Sketch the conic. 2 3 + 3 sine
(a) Find the eccentricity, (b) Identify the conic, (c) Give an equation of the directrix, and (d) Sketch the conic. 2 + sine
(a) Find the eccentricity, (b) Identify the conic, (c) Give an equation of the directrix, and (d) Sketch the conic. 4 5 - 4 sine
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
Write a polar equation of a conic with the focus at the origin and the given data.Parabola, vertex (3, π/2)
Write a polar equation of a conic with the focus at the origin and the given data.Ellipse, eccentricity 0.6, directrix r = 4 csc θ
Write a polar equation of a conic with the focus at the origin and the given data.Ellipse, eccentricity 2/3, vertex (2, π)
Write a polar equation of a conic with the focus at the origin and the given data.Hyperbola, eccentricity 3, directrix x = 3
Write a polar equation of a conic with the focus at the origin and the given data.Hyperbola, eccentricity 1.5, directrix y = 2
Write a polar equation of a conic with the focus at the origin and the given data.Parabola, directrix x = -3

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