≪ View Page

Search

You can find the results of your search below.

Fulltext results:

MTH321: Real Analysis I (Spring 2020)
19 Hits, Last modified:
Define bounded sequence. * 2.07- Prove that $\{\frac{1}{n}\}$ is decreasing sequence. * 2.08- Prove that $\{1+\frac{1}{n}\}$ is a decreasing sequence. * 2.09- Prove that $\{\frac{n+1}{n+2}\}$ is increasing sequence. * 2.10- Is the sequence $\{\frac{n+2}{n}\}$ is increasing or decreasing sequence?
MTH322: Real Analysis II (Fall 2021)
17 Hits, Last modified:
e 0$ for $x\ge a$. If $\lim\limits_{x\to \infty }\frac{f(x)}{g(x)}=1$, then $\int\limits_{a}^{\infty }{... theorem to prove that $\int\limits_{0}^{\infty }{\frac{\sin x}{x}\,dx}$ is convergent. - Use Dirichlet... o prove that $\int\limits_{0}^{\infty }{{e}^{-x} \frac{\sin x}{x} dx}$ is convergent. - Discuss the co... a sequence of function $\{f_n\}$, where $f_n(x)=\frac{nx}{1+n^2 x^2}$, for all $x\in\mathbb{R}$. Prove
MTH321: Real Analysis I (Fall 2021)
14 Hits, Last modified:
Define bounded sequence. * 2.07- Prove that $\{\frac{1}{n}\}$ is decreasing sequence. * 2.08- Prove that $\{1+\frac{1}{n}\}$ is a decreasing sequence. * 2.09- Prove that $\{\frac{n+1}{n+2}\}$ is increasing sequence. * 2.10- Is the sequence $\{\frac{n+2}{n}\}$ is increasing or decreasing sequence?
MTH604: Fixed Point Theory and Applications (Spring 2020)
10 Hits, Last modified:
ric and $T:X\to X$ be a mapping defined by $T(x)=\frac{10}{11}\left(x+\frac{1}{x} \right)$ for all $x\in X$. Prove that $T$ is a contraction mapping with Lipschitz constant $\alpha=\frac{10}{11}$. - Let $X=[0,1]$ be a metric space wit... ric and $T:X\to X$ be a mapping defined by $T(x)=\frac{1}{7}(x^3+x^2+1)$ for all $x\in X$. Prove that $T
MTH322: Real Analysis II (Spring 2023)
8 Hits, Last modified:
ble functions for $x>a$. If $\lim_{x\to \infty } \frac{f(x)}{g(x)}=0$, then convergence of $\int_{a}^{\... at for all $n\in \mathbb{N}$, we have $$E_n(x)=1+\frac{x}{1!}+\frac{x^2}{2!}+... +\frac{x^n}{n!}\quad \hbox{for all } x\in\mathbb{R}.$$ - Consider a sequence of function
MTH604: Fixed Point Theory and Applications (Fall 2022)
4 Hits, Last modified:
$F$ has attracting fixed point. - Prove that $\frac{1}{2}e^x \cos(x)$ has attracting fixed point in t... tration, then prove that $\{d(F^m(x),F^n(x) \leq \frac{L^n}{1-L}d(x,F(x) \}$ for $m>n$, $n\in \{1,2,...\... . - Prove that $G$ is contraction, where $G(x)=\frac{x+F(x)}{2}$, on $X$ if $F$ is contraction on $X$.... \overline{B}_r \to \overline{B}_r$, where $G(x)=\frac{x+F(x)}{2}$. ===== Resources ===== * {{ :atiq:
MTH251: Set Topology
2 Hits, Last modified:
n $\mathbb{R}$? * Consider the set $A=\left\{1,\frac{1}{2},\frac{1}{3},... \right\}$. Find the derive set of $A$ under usual topology. * Define closure of
MTH604: Fixed Point Theory and Applications
2 Hits, Last modified:
d open ball, closed ball and sphere with radius $\frac{1}{2}$ and center $1$. * Define fixed point wit... f the function $F(x)=\cos x$ in the interval $[0,\frac{\pi}{2}]$. * Find fixed point of the function $
MTH321: Real Analysis I (Spring 2023)
2 Hits, Last modified:
en there exists a point $c\in (a,b)$ such that $\frac{f(b)-f(a)}{b-a}={f}'(c)$. - If $f$ and $g$ are ... o different limits. - Write a reason that $\{n+\frac{1}{n} \}$ is not Cauchy sequence. ====Online re
MATH-510: Topology
1 Hits, Last modified:
u$? - Write the closure of the set $S=\left\{1+\frac{1}{n}: n \in \mathbb{N} \right\}$ in usual topolo
MCQs or Short Questions @atiq:sp15-mth321
1 Hits, Last modified:
divergent. * (D) bounded. - A sequence $\{\frac{1}{n} \}$ is * (A) bounded. * (B) unbound