For problems 7 & 8 give a power series representation for the integral of the following function. 7x 7. h (x) = 3 – 6x

Q: where f(x) = 5 x^ by identifying it as the value of a derivative or integral of geometric series. as…

A: Given that: fx=∑n=0∞xn Which is the sum of geometric series. Derivative of the function is:…

Q: 5. Solve for x² − x+6 x³ + 3x 1³ dx.

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Q: 00 If f(r) = > 2x" and g(x) na", find the power series of f(r)g(x). %3D n=0 00

A: We have to find product of two power series.

Q: 8. 4 x dx = 7.5 x2dx =2

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Q: Let f(x) = √ sin t dt. t This is called the sine integral and is denoted Si(z). (a) Replace sin(t)…

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Q: If n=10 and p=0.5, find P(x=8) Give at least 4 decimal places.

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Q: Express the function as the sum of a power series by first using partial fractions. f(x) =  8 x2 −…

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Q: f (x) = arctan(r²)

A: We know that power series of arctan(x)

Q: Use the exponential series to find an approximation to e-1 correct to three significant figures.

A: we know that,ex=∑n=0∞x2n!⇒ex=1+x1!+x22!+x33!+x44!+x55!+x66!+x77!+x88!+···putting…

Q: Express the series as a rational function. n=1

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Q: 4. √ (3x² + 4x − 5). 8(r³+2x²–5x+5) dx

A: We have to find solutions

Q: 2.x 7. Use the Maclaurin series for f(x) = e2x to estimate edx to two decimal digit accuracy.

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Q: 16. Find a power series centered at zero for f(x) = 3-4x5

A: Just answering this to check if i am able to submit the answers or not. Please don't review this…

Q: 353. y = x-1/2 (x² + 3)2 (3x – 4)ª

A: First, we expand the given expression using properties of logarithm