Exam 37: Infinite Series

Compute the value of $e^{1.2}$ , to three decimal places, using three terms of the Taylor's series expanded about $\mathrm{a}=1$ .

Does the function below have half-wave symmetry?

Find the first four terms (rounded to three decimal places) of the Fourier series. Assume half-wave symmetry. 3 6 9 12 16 18 0 3.1 4.5 8.1 15.1 14.4 0

Find the first four terms of the Maclaurin series for the function: $y=x^{2} e^{x}$

Use the ratio test to determine if the series converges: $1+\frac{3}{2}+\frac{9}{8}+\frac{27}{48}+\ldots+\frac{3^{n}}{2^{n} n !}+\ldots$

Evaluate the integral to three decimal places by integrating the first three terms of the series: $\int_{0}^{1 / 4} e^{\sqrt{x}} d x$

Use the series for $\cos x$ to find the series for $\cos \sqrt{x}$ .

Write a Fourier series for the waveform below:

Use the ratio test to determine if the series converges of diverges: $2+2+\frac{4}{3}+\frac{2}{3}+\ldots+\frac{2^{n}}{n !}+\ldots$

Use the ratio test to determine if the following series converges or diverges: $\frac{6}{5}+\frac{12}{25}+\frac{24}{125}+\frac{48}{625}+\ldots$

Compute the value of the following expression, to three decimal places, using three terms of the appropriate Taylor's series: $\ln 0.97$

Find the first six terms (rounded to three decimal places) of the Fourier series. Assume half-wave symmetry. 2 4 6 8 10 12 14 16 18 0 2.1 4.8 7.5 11.2 10.9 6.8 5.2 2.4 0

Find the first four terms of the Maclaurin series for the function: $f(x)=\ln (3 x+1)$

Write a Fourier series for the function below:

Find the first six terms (rounded to three decimal places) of the Fourier series. Assume half-wave symmetry. 2 4 6 8 10 12 14 16 18 0 4 7.5 10 8 6.5 5 4 2 0

Find the series for $x e^{x^{2}}$ by differentiating $e^{x^{2}}$ and multiplying by the appropriate factor.

Verify that the first four terms of the Fourier series for the sawtooth function below are: $f(t)=\frac{1}{2}-\frac{1}{\pi}\left[\sin 2 \pi t+\frac{1}{2} \sin 4 \pi t+\frac{1}{3} \sin 6 \pi t\right]$

Multiply the appropriate series to obtain the series for $e^{2 x} \cos 2 x$ .

Find the series for $\frac{x}{(1+x)^{2}}$ by differentiating $\frac{1}{1+x}$ and multiplying the related series by an appropriate factor.

Write a Fourier series for the function below: