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mathematics
calculus 6th edition

Questions and Answers of Calculus 6th edition

Determine whether the series is absolutely convergent, conditionally convergent, or divergent. Σ m=1 10" (n + 1)4²n+1
Test the series for convergence or divergence. 00 n=1 2 3″ n² n!
Find the radius of convergence and interval of convergence of the series. 2n Σ (-1)*. (2n)! n=0
Determine whether the series is convergent or divergent. (-1)" Σ *=1 vn + 1 n+1
Test the series for convergence or divergence. 00 Σ (-1)*-1. n=1 In n n
Test the series for convergence or divergence. 00 sin 2n Σ "=11+ 2"
Determine whether the series is absolutely convergent, conditionally convergent, or divergent. 00 Σ (-1)*+1. n! n=1 n²2"
Determine whether the series is convergent or divergent. 1 5 8 + 11 14 + 17
Find the radius of convergence and interval of convergence of the series. (x - 2)" Σ nào n+1
Find the Taylor series for f(x) centered at the given value of a. [Assume that f has a power series expansion. Do not show that Rn(x) → 0.]f(x) = x – x3, a = –2
Test the series for convergence or divergence. 00 Σ n=1 Η COS NTT 3/4
Determine whether the series is absolutely convergent, conditionally convergent, or divergent. Σ n=1 (-1)" aretan n 71 71
Test the series for convergence or divergence. Σ 71=0 n! 2 5 8 (3n+2)
Find the radius of convergence and interval of convergence of the series. (x − 3)" 2n + 1 Σ (-1)". n=0
Test the series for convergence or divergence. 00 Σ sin(nm/2) n!
Determine whether the series is absolutely convergent, conditionally convergent, or divergent. 3 – cos n Σ 2/3-2 n=171
Find the radius of convergence and interval of convergence of the series. 00 Σ n=1 3*(x + 4)" 'n
Test the series for convergence or divergence. n² + 1 Σ n=1n3 + 1
Test the series for convergence or divergence. ∑ (-1)" sin n=1 ㅠ n
Determine whether the series is convergent or divergent. Σ n=1 5-2√√n 3 H
Find the Taylor series for f(x) centered at the given value of a. [Assume that f has a power series expansion. Do not show that Rn(x) → 0.]f(x)= ex, a = 3
Determine whether the series is convergent or divergent. Σ 1n n=1 n 3n + 1
Determine whether the sequence converges or diverges. If it converges, find the limitan = 1 – (0.2)n
Determine whether the series is convergent or divergent. Π ne n3 Σ n=1 n + 1 +1
Determine whether the series is convergent or divergent. Σ cos 3n 1 + (1.2)"
Find the Taylor series for f(x) centered at the given value of a. [Assume that f has a power series expansion. Do not show that Rn(x) → 0.]f(x) cos x, a = π
Find the radius of convergence and interval of convergence of the series.
Determine whether the series is convergent or divergent. n 2n Σ n=1 (1 + 2n²)"
Determine whether the series is convergent or divergent. 00 Σ 3n + 2 S n(n + 1)
Test the series for convergence or divergence. 00 ∑ (-1)" cos n=1 티 n
Determine whether the series is absolutely convergent, conditionally convergent, or divergent. 00 n=1 712 게 7'
Test the series for convergence or divergence. (-1)"-1 Σ n=2 Vn – 1 √n. -
Find the Taylor series for f(x) centered at the given value of a. [Assume that f has a power series expansion. Do not show that Rn(x) → 0.]f(x) = sin x, a = π/2
Find the radius of convergence and interval of convergence of the series. 00 n=1 (x - 2)" 71 n'
Determine whether the series is convergent or divergent. 00 n=1 In n 3 n
Determine whether the series is convergent or divergent. Σ n=1 1.3.5. . (2n-1) 5*n!
Ifhas positive radius of convergence andshow that ΜΙ f(x) = Sm= Emo Cmax –
Test the series for convergence or divergence. 00 Τ Π Σ (−1)". n! n=1
Determine whether the series is absolutely convergent, conditionally convergent, or divergent. Σ n=1 cos(nπ/3) n!
Test the series for convergence or divergence. 2 Σ (−1)". n=1 In n
Find the radius of convergence and interval of convergence of the series. Σ n=1 (3x – 2)" η 3η
Find the Taylor series for f(x) centered at the given value of a. [Assume that f has a power series expansion. Do not show that Rn(x) → 0.]f(x) = 1/√x, a = 9
Find a power series representation for f, and graph f and several partial sums sn(x) on the same screen. What happens as n increases?f(x) = x/x2 + 16
Test the series for convergence or divergence. Σ n=1 n 5 71
Determine whether the series is convergent or divergent. (-5) ²n Σ n29" n=1
Find the radius of convergence and interval of convergence of the series. 0 < 9 - - "=1 b" ( 4 x).
Test the series for convergence or divergence. Σ k=1 k + 5 5k
Find the Taylor series for f(x) centered at the given value of a. [Assume that f has a power series expansion. Do not show that Rn(x) → 0.]f(x) = x–2, a = 1
Find a power series representation for f, and graph f and several partial sums sn(x) on the same screen. What happens as n increases?kf(x) = ln(x2 + 4)
Determine whether the sequence converges or diverges. If it converges, find the limit.an = e1/n
Determine whether the series is convergent or divergent. Σ (-1)*1. n=1 n n + 1
Find the length of the curve.y = 1 + 6x3/2, 0 ≤ x ≤ 1
Find the length of the curve.y2 = 4(x + 4)3, 0 ≤ x ≤ 2, y > 0
Evaluate the integral.∫(x2 – bx) sin 2x dx
Evaluate the integral. X 1 + x³ 3 xp.
Evaluate the integral. sec x cos 2x - dx sin x + sec x
Evaluate the integral. sin x cos x sin*x + cos*x dx
Evaluate the integral.∫x sin2x cos x dx
Set up, but do not evaluate, an integral for the area of the surface obtained by rotating the curve about (a) The x-axis and(b) The y-axis.y = x4, 0 ≤ x ≤ 1
Use the arc length formula to find the length of the curve y = √2 – x2, 0 ≤ x ≤ 1. Check your answer by noting that the curve is part of a circle.
Set up, but do not evaluate, an integral for the area of the surface obtained by rotating the curve about (a) The x-axis and(b) The y-axis.y = xe–x, 1 ≤ x ≤ 3
Set up, but do not evaluate, an integral for the length of the curve.y = cos x, 0 ≤ x ≤ 2π
Set up, but do not evaluate, an integral for the area of the surface obtained by rotating the curve about (a) The x-axis and(b) The y-axis.y = tan–1 x, 0 ≤ x ≤ 1
Set up, but do not evaluate, an integral for the length of the curve.y = x–x2, 0 ≤ x ≤ 1
Set up, but do not evaluate, an integral for the area of the surface obtained by rotating the curve about (a) The x-axis and(b) The y-axis.x = √y – y2
Let f(x) = xe–x if x ≥ 0 and f(x) = 0 if x < 0. (a) Verify that f is a probability density function.(b) Find P(1 ≤ x ≤ 2).
Let f(x) = c/(1 + x2). (a) For what value of c is f a probability density function? (b) For that value of c, find P(–1 < X < 1).
Set up, but do not evaluate, an integral for the length of the curve.x = y + y3, 1 ≤ y ≤ 4
Set up, but do not evaluate, an integral for the length of the curve.x2/a2 + y2/b2 = 1
Find the length of the curve.x = 1/3√y(y − 3), 1 ≤ y ≤ 9
Find the length of the curve.y = 3 + 1/2cosh 2x, 0 ≤ x ≤ 1
Find the length of the curve.y = ln(1 – x2), 0 ≤ x ≤ 1/2
Sketch the region bounded by the curves, and visually estimate the location of the centroid. Then find the exact coordinates of the centroid.y = 4 – x2, y = 0
Sketch the region bounded by the curves, and visually estimate the location of the centroid. Then find the exact coordinates of the centroid.3x + 2y = 6, y = 0, x = 0
Sketch the region bounded by the curves, and visually estimate the location of the centroid. Then find the exact coordinates of the centroid.y = 1/x, y = 0, x = 1, x = 2
Find the centroid of the region bounded by the given curves.y = x2, x = y2
Find the centroid of the region bounded by the given curves.y = x + 2, y = x2
Solve the differential equation.kdy/dx = y/x
Determine whether the differential equation is linear.y' + cos x = y
Solve the differential equation.dy/dx = √x/ey
Determine whether the differential equation is linear.y' + cos y = tan x
Solve the differential equation.(x2 + 1)y' = xy
Determine whether the differential equation is linear.yy' + xy = x2
Solve the differential equation.y' = y2 sin x
Determine whether the differential equation is linear.xy + √x = exy'
Solve the differential equation.(1 + tan y)y' = x2 + 1
Solve the differential equation.y' + 2y = 2ex
Solve the differential equation.du/dr = 1 + √r/1 + √u
Solve the differential equation.y' = x + 5y
Solve the differential equation.dx/dt = 1 – t + x – tx
Solve the differential equation.xy' – 2y = x2
Solve the differential equation.dy/dt = tet/y√1 + y2
Solve the differential equation.2yey2y' = 2x + 3√x
Solve the differential equation.dy/dθ = eysin2θ/y sec θ
Solve the differential equation.x2y' + 2xy = cos2 x
Solve the differential equation.du/dt = 2 + 2u + t + tu
Solve the differential equation.xy' + y = √x
Solve the differential equation.y' + y = sin(ex)
Solve the differential equation.sin x + dy/dx + (cos x)y = sin(x2)
Find the solution of the differential equation that satisfies the given initial condition.dy/dx = x/y, y(0) = –3

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