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mathematics
precalculus

Questions and Answers of Precalculus

Test the series for convergence or divergence.
Test the series for convergence or divergence.
Test the series for convergence or divergence. Σ (-1)"1ne " пе n+1 -η n=1
Test the series for convergence or divergence. n? n+1 3 n' + 4 n=1
Test the series for convergence or divergence.
Test the series for convergence or divergence.
Test the series for convergence or divergence.
Test the series for convergence or divergence. ο0 n+1 Σ Vn + 1 n=0 ν
Test the series for convergence or divergence. In 4 In 5 In 3 In 6 In 7
Test the series for convergence or divergence. 10 9. 0ol00 N/5
Test the series for convergence or divergence. 2 11 3
For what values of p does the series converge? E-2 1/(nº In n) n=2
The meaning of the decimal representation of a number 0.d1d2d3 . . . (where the digit di is one of the numbers 0, 1, 2, . . . , 9) is that di d2 0.d, d2dzd4 ... dz d4 10 102 103 104
Use the sum of the first 10 terms to approximate the sum of the series. Estimate the error. ο0 Σ 3" + 4" n=1
Use the sum of the first 10 terms to approximate the sum of the series. Estimate the error. ,1/n 00 п п
Use the sum of the first 10 terms to approximate the sum of the series. Estimate the error. ο Σ 5 + n° η-1
Determine whether the series converges or diverges. Σ 1+1/n n=1 n
Determine whether the series converges or diverges. 2 sin п n=1
Determine whether the series converges or diverges.
Determine whether the series converges or diverges. п! п31
Determine whether the series converges or diverges. 1/л п п%31
Determine whether the series converges or diverges. 2 Σ 1 - -n п n=1
Determine whether the series converges or diverges. 1 Σ п-2 пуп? — 1
Determine whether the series converges or diverges. e" + 1 Σ п-1 пе" + 1 00
Determine whether the series converges or diverges.
Determine whether the series converges or diverges. 5 + 2n Σ (1 + n?)? 2 n=1
Determine whether the series converges or diverges. n + 2 Σ (n + 1)³ n=3
Determine whether the series converges or diverges. V1 + n 2 + n n=1
Determine whether the series converges or diverges. п? +п + 1 п* + n? п31
Determine whether the series converges or diverges. п+1 Σ п-1 n' + п
Determine whether the series converges or diverges. Σ /n + 2 n=1
Determine whether the series converges or diverges.
Determine whether the series converges or diverges. 4"+1 3" – 2 п-1
Determine whether the series converges or diverges. УЗп + 1 3n п31
Determine whether the series converges or diverges.
Determine whether the series converges or diverges. (2k – 1)(k² – 1) (k + 1)(k² + 4)² k=1
Determine whether the series converges or diverges. k=1 k3 + 4k + 3
Determine whether the series converges or diverges. k sin?k .3 k-1 1 + k³ k=1
Determine whether the series converges or diverges. In k 00 k=1
Determine whether the series converges or diverges. 6" 5" – 1 п3
Determine whether the series converges or diverges. п — 1 Σ 3 п31 п' + 1
Determine whether the series converges or diverges. Σ п п-2
Determine whether the series converges or diverges. 8 1 n-1 n +8
Find all values of c for which the following series converges. ο0 Σ n + 1 n=1 η
How many terms of the series would you need to add to find its sum to within 0.01? 2-2 1/[n(ln n)*] n=2
Find the sum of the series correct to four decimal places. —2п -1 пе
Find the values of p for which the series is convergent. In n n=1__nº
Find the values of p for which the series is convergent. Σ п n=3 n In n [In(ln n)]P
Explain why the Integral Test can’t be used to determine whether the series is convergent. cosʻn + n° n=1 1 + n?
Determine whether the series is convergent or divergent. п Σ п* + 1 п-1
Determine whether the series is convergent or divergent. 00 Σ n=1 n- + n° 3
Determine whether the series is convergent or divergent. Σ ke-kt k=1
Determine whether the series is convergent or divergent. Σ kek k=1
Determine whether the series is convergent or divergent. In n 2 n=2 n
Determine whether the series is convergent or divergent. 00 n=2 n In n п
Determine whether the series is convergent or divergent. Зп — 4 Σ 2n п-3 п
Determine whether the series is convergent or divergent. 3 п Σ n* + 4
Determine whether the series is convergent or divergent. 00 n2 + 2n + 2 n=1
Determine whether the series is convergent or divergent. 1 Σ n² + 4 п n=1
Determine whether the series is convergent or divergent. п Σ 1+ п3/2 п31 N32
Determine whether the series is convergent or divergent. Уп + 4 Σ 00 ,2 n²
Determine whether the series is convergent or divergent. 1 4V4 3/3 2/2 5/5
Determine whether the series is convergent or divergent. 1 1 11 3 15 19
Determine whether the series is convergent or divergent. 1 - + .. 5 11 13
Determine whether the series is convergent or divergent. 1 27 64 125
Determine whether the series is convergent or divergent. 00 Σ . n-0.9999 n=3
Determine whether the series is convergent or divergent. n=1 n
Plot the point whose polar coordinates are given. Then find two other pairs of polar coordinates of this point, one with r > 0 and one with r > 0.(a) (1, π/4) (b) (-2, 3π/2) (c) (3,
Sketch the curve with the given polar equation by first sketching the graph of r as a function of θ in Cartesian coordinates.r = 2 cos 4θ
Sketch the curve with the given polar equation by first sketching the graph of r as a function of θ in Cartesian coordinates.r = -sin 5θ
Sketch the curve with the given polar equation by first sketching the graph of r as a function of θ in Cartesian coordinates.r = 3 cos 3θ
Sketch the curve with the given polar equation by first sketching the graph of r as a function of θ in Cartesian coordinates. r ?, -2 S 0 < 2n = 0°
Sketch the curve with the given polar equation by first sketching the graph of r as a function of θ in Cartesian coordinates.r = 1 + 2 cos θ
Sketch the curve with the given polar equation by first sketching the graph of r as a function of θ in Cartesian coordinates.r = 1 - cos θ
For each of the described curves, decide if the curve would be more easily given by a polar equation or a Cartesian equation. Then write an equation for the curve.(a) A circle with radius 5 and
Find a polar equation for the curve represented by the given Cartesian equation.x2 - y2 = 4
Find a polar equation for the curve represented by the given Cartesian equation.x2 + y2 = 2cx
Find a polar equation for the curve represented by the given Cartesian equation.4y2 = x
Find a polar equation for the curve represented by the given Cartesian equation.y = 1 + 3x
Find a polar equation for the curve represented by the given Cartesian equation.y = x
Find a polar equation for the curve represented by the given Cartesian equation.y = 2
Identify the curve by finding a Cartesian equation for the curve.r2 sin 2θ = 1
Identify the curve by finding a Cartesian equation for the curve.17. r = 5 cos θ
Identify the curve by finding a Cartesian equation for the curve.r 2 = 5
Find the distance between the points with polar coordinates4, 4π/3d and 6, 5π/3d.
Sketch the region in the plane consisting of points whose polar coordinates satisfy the given conditions. r> 1, T< 0 < 2m
Sketch the region in the plane consisting of points whose polar coordinates satisfy the given conditions. r>0, п/4 < ө < Зп/4
Sketch the region in the plane consisting of points whose polar coordinates satisfy the given conditions. 0
Sketch the region in the plane consisting of points whose polar coordinates satisfy the given conditions.r > 1
The Cartesian coordinates of a point are given.(i) Find polar coordinates (r, θ) of the point, where r > 0 and 0 < θ, 2π.(ii) Find polar coordinates (r, θ) of the point, where r <
Plot the point whose polar coordinates are given. Then find the Cartesian coordinates of the point.(a) (4, 4π/3) (b) (-2, 3π/4) (c) (-3, -π/3)
Plot the point whose polar coordinates are given. Then find the Cartesian coordinates of the point.(a) (2, 3π/2) (b) (√2, π/4) (c) (-1, -π/6)
Plot the point whose polar coordinates are given. Then find two other pairs of polar coordinates of this point, one with r > 0 and one with r > 0.(a) (2, 5π/6) (b) (-2, 3-2π/3) (c)
Find the solution of the differential equation that satisfies the given initial condition.dy/dx = x sin x/y, y (0) = -1
Find the solution of the differential equation that satisfies the given initial condition.dY/dX + xey , y(0)= 0
Solve the differential equation.dz/dt + et+z = 0 dz + e+: = 0 dt
Solve the differential equation.dp/dt = t2p - p + t2 - 1
Solve the differential equation.dH/dR = RH2 √1 + R2/In H
Solve the differential equation.dθ/dt = t secθ/θet2
Solve the differential equation.du/dt = 1 + t4/ut2 + u4t2

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