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Section 7.4 Additional Problems
Problem 7.4.1 .
Find the Integral form, Lagrange form, and Cauchy form of the remainder for Taylor series for the following functions expanded about the given values of \(\,a\text{.}\)
(a)
\(f(x)=e^x\text{,}\) \(a=0\)
(b)
\(f(x)=\sqrt{x}\text{,}\) \(a=1\)
(c)
\(f(x)=(1+x)^\alpha\text{,}\) \(a=0\)
(d)
\(f(x)=\frac{1}{x}\text{,}\) \(a=3\)
(e) \(f(x)=\ln x,\ a=2\)
(f) \(f(x)=\cos x, a=\frac{\pi}{2}\)
