Mathematics
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user381164
  • Member for 7 years, 1 month
  • Last seen more than 7 years ago
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All Questions Answers
Score Newest
question
4
If $f$ is continuous and with a limit at infinity then $f$ is uniformly continuous
Nov 7, 2016
question
3
Show that the equation $6x^4-7x+1=0$ has at most 2 real roots.
Oct 28, 2016
question
2
Let $f : \mathbb{R} \rightarrow \mathbb{R}$, differentiable. Suppose that $f'(x) ≥ 1$, for all $x > 0$. Show that $f'(0) ≥ 1$
Oct 28, 2016
question
2
Let $f,g : [a,b] \rightarrow \mathbb{R}$, continuous on $[a,b]$ and differentiable on (a,b). Show that there exists $\phi$ s.t $f'(\phi) = g'(\phi)$
Oct 28, 2016
question
1
Show that if two maximal values are equal on continuous functions, then there exists $\psi \in [a,b]$ with $f(\psi) = g(\psi)$
Oct 21, 2016
question
1
Show that the function $\cos: \mathbb{R} \rightarrow \mathbb{R}$ that sends each $x \in \mathbb{R}$ to $\cos x$, is Lipschitz continuous
Oct 21, 2016
question
1
Use L'Hopital's rule to show that $\lim_{x \rightarrow+\infty} \frac{f(x)}{g(x)}= \ell$
Oct 28, 2016
question
1
Let $f : (1, +\infty) \rightarrow \mathbb{R}$ be differentiable s.t $|f'(x)| ≤ 1/x$ for all $x > 1$. Show that $(f(x + \sqrt{x}) - f(x)) = 0$
Oct 28, 2016
question
1
Let $f : [0, +\infty) \rightarrow \mathbb{R}$ be uniformly continuous. Show that $f$ has sublinear growth [duplicate]
Nov 4, 2016
question
1
$f$ is uniformly continuous if and only if the limits exist in $\mathbb{R}$
Nov 4, 2016

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