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Real Analysis
For the functions
f(x) = x^2+1
g(x) = (e(x))/(x-1)
Calculate (f ∘ g)(x) & (g ∘ f)(x)
What are the Domains of (f ∘ g)(x) & (g ∘ f)(x)
f(x) = x^2+1
g(x) = (e(x))/(x-1)
Calculate (f ∘ g)(x) & (g ∘ f)(x)
What are the Domains of (f ∘ g)(x) & (g ∘ f)(x)
Real Analysis
If the co-domain does not contain all the elements of range , can it be a function?
like co-domain {3,4,5,6,7}
range {3,4 11}. normally we know range is a subset of co-domain. but here it does not . so is it possible?
like co-domain {3,4,5,6,7}
range {3,4 11}. normally we know range is a subset of co-domain. but here it does not . so is it possible?
Real Analysis
what is the domain and range of sqrt of {(x-1)/(x+2)}
Real Analysis
Test the following series for convergence:
a) ∑(n goes from 1 to infinity) n^(1/n).
b)∑(n goes from 1 to infinity) (((-1)^n)sin(3n x))/n^3
a) ∑(n goes from 1 to infinity) n^(1/n).
b)∑(n goes from 1 to infinity) (((-1)^n)sin(3n x))/n^3
Real Analysis
Show that: ∑(n goes from 0 to ∞)1/((α+n)(α+n+1)) =1/α , for α>0.
Real Analysis
What is the derivative of a function f(x) at a point c given by?
Real Analysis
What does Rolle's Theorem state?
Real Analysis
Suppose that f is defined on a deleted neighborhood of x0. Denote by
D(f) the domain of f. Show that the following statements are equivalent:
a) lim x -> x0 = L
b) whenever {uk} is a sequence in D(f) \ {x0} that converges to x0, then the sequence {f(uk)} converges to L
D(f) the domain of f. Show that the following statements are equivalent:
a) lim x -> x0 = L
b) whenever {uk} is a sequence in D(f) \ {x0} that converges to x0, then the sequence {f(uk)} converges to L
Real Analysis
Suppose that S is contained in R and that S is not closed. Is it true that there is a subsequence in S that converges to some x not in S?
Real Analysis
Prove [0,1] is not countable without using the outer measure of an interval is its length?
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#332078 on Oct 2022
#332078 on Oct 2022