Course 45334

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Determine how many terms should be used to estimate the sum of the entire series with an error of less than 0.001.

n ≥ 31

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n ≥ 13

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n ≥ 14

✅

n ≥ 15

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Estimate the magnitude of the error involved in using the sum of the first four terms to approximate the sum of the entire series.

<

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< 1.37 × 10^-3

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< 1.23 × 10^-2

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< 4.12 × 10^-3

✅

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Solve the differential equation subject to the initial condition.

+ 10xy - e^-5x2 = 0; y(0) = 4

y = (x + 4)e^-5x2

✅

y = (x + 4)e^-5x

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y = xe^-5x2 + 4

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y = xe^-5x + 4

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Solve the differential equation subject to the initial condition.

x + (1 + x)y = 1; y(5) = 2

y =

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y =

0%

y =

✅

y =

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Find the general solution for the differential equation.

x² + xy = 4x⁴ + 7x⁷, x > 0

y = k

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y = x⁴ + x⁷ +

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y = x³ + x⁶ +

✅

y = x⁴ + x⁷ + C

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Find the particular solution for the initial value problem.

(4x + 4)y = ; y(0) = 1

y = e^{2x2 + 4x}

✅

y = e^{4x2 + 4x}

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y = e^{2x2 + 4x + 1}

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y = e^{4x2 + 4x} + 1

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Find the general solution for the differential equation.

= y²(4 - e^x)

y =

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y =

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y =

✅

y = 4x - e^x + C

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Find the particular solution for the initial value problem.

x = 4x²e2x; y(0) = 16

y = 4xe2x - 2e2x + 18

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y = 2xe2x + 16

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y = 4xe2x - e2x + 17

0%

y = 2xe2x - e2x + 17

✅

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