Approximate the following functions using Taylor series. Solve the absolute and relatice error in each item when x = 3

Q: series to approximate the definite integral I to within the indicated accuracy. [0.5 x³e-x² dx…

A: Series approximation

Q: Calculate the third term of the power series of sin x if x = 1.5. Answer.

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Q: Given the function f(x) = 3x² - 8x + 8. Calculate the following values: f(-2)= f(-1) = f(0) f(1) =…

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Q: A population of a town grows according to the law of uninhibited growth modeled by the function P(t)…

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Q: Solve until the 6th derivative and provide the SUMMATION NOTATION of the taylor series as the final…

A: The Taylor's series expansion of a function f(z) about z=a is given by the equation;…

Q: t taken for an investment to increase by 20% when the interest rate is 6% is given by t= ln1.2/0.06.…

A: The time t taken for an investment to increase by 20% when the interest rate is 6% is given by…

Q: and/or provide an explanation for credit.

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Q: Solve until the 6th derivative and provide the summation of the taylor series. f(x) = ln 4x ; c = ¼

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Q: For the logistic difference equation xt+1 = cxt(1 − xt) with x0 = 0.875 and c = 3.5, calculate xt to…

A: xt+1=cxt(1-xt) with x0=0.875 and c=3.5

Q: Observe the function X f(x) = (1+2x)² In order to find the power series for this function, complete…

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Q: Find a formula for f n  x if fx = ln (x-1)

A: Given, f(x)=ln(x-1) differentiate with respect to x, f'(x)=1x-1 Again differentiate with respect to…

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: (14). . Find the first fuer terms of the Taylor Series for the function flx)= ex9 ○メ=o.

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Q: Find the half-range sine series for the function f(t)=nt-t², in the interval 0<t<n.

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Q: Find the first four terms for this function using the MacLaurin series table: f(x)=sin(3x)

A: Maclaurin series

Q: 1+x Show that coth-1x = ; In () 2 x-1

A: We have to prove the given expression.

Q: The series are connected with inductance 350 henry, and the resistance is 18 ohms. Find I(t) if the…

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