Let f(x) and g(x) be analytic at x0. Determine whether the

Chapter 8, Problem 36E

(choose chapter or problem)

Let $f(x) \text { and } g(x)$ be analytic at $x_{0}$. Determine whether the following statements are always true or sometimes false:

(a) $3 f(x)+g(x)$ is analytic at $x_{0}$

(b) $f(x) / g(x) $ is analytic at $x_{0}$

(d) ${[f(x)]^{3}-\int_{x_{0}}^{x} g(t) d t}$ is analytic at $x_{0}$

Equation Transcription:

$f(x)\ and\ g(x)$

${x}_{0}$

$3f(x)+g(x)$

${x}_{0}$

$f(x)/g(x)$

${x}_{0}$

$f'(x)$

${x}_{0}$

$[f(x){]}^{3}-\int\limits_{{x}_{0}}^{x}g(t)dt$

${x}_{0}$

Text Transcription:

f(x) and g(x)

x_0

3 f(x)+g(x)

x_0

f(x) / g(x)

x_0

f^\prime(x)

x_0

f(x)]^3-\int_x_0^x g(t) d t

x_0

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