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Real Analysis
Prove osc(f+g),S) <= osc(f,S) + osc(g,S)
Real Analysis
Let f:[a,b]->Real Numbers R be integrable and c be an element of the Real Numbers R. Show that cf is integrable and
integral from a to b of cf(x)dx= c*integral from a to b of f(x)dx.
integral from a to b of cf(x)dx= c*integral from a to b of f(x)dx.
Real Analysis
if f:[a,b]->R is integrable, show that the restriction of f to any interval [c,d] subset of [a,b] is integrable.
Real Analysis
Show in detail that the integral from 0 to 1 of x^2dx= 1/3.
Real Analysis
Prove: If f and g are differentiable and a is in the real numbers, then (fg)'(a) = f(a)g'(a) + f'(a)g(a) and (f/g)'(a) = (g(a)f'(a)-f(a)g'(a))/g(a)^2.
Real Analysis
Find the maclaurin series for sinx and cosx and show that they converge for all x to their respective functions.
Real Analysis
Use Taylor's theorem with n=3 to find an estimate for square root of 65 and give an estimate of the error.
Real Analysis
suppose f has the property that there is a number a>1 so that for any x and y in the domain of f, |f(x)-f(y)|<=|x-y|^a. Show that f is contstant.
Real Analysis
if f(x)=x^n, where n is an element of N, show that f'(a)=na^n-1 for any a.
Real Analysis
if f(x)=x, show that f'(a)=1 for all a.
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#332078 on Oct 2022
#332078 on Oct 2022