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Real Analysis: Short Questions and MCQs @msc:mcqs_short_questions
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convergent. - Prove that $\left\{\frac{1}{n+1} \right\}$ is decreasing sequence. - Is the sequence $\left\{\frac{n+2}{n+1} \right\}$ is increasing or decreasing? - If the sequen... $(1,2)$ * (B) $\left(\frac{1}{2},\frac{1}{3} \right)$ * (C) $[3. \pi]$ * (D) $(2\pi,180)$ \\ ... anel> <panel> 5. A sequence $\left\{\dfrac{1}{n} \right\}$ is * (A) bounded. * (B) unbounded.
Chapter 02 - Sequence and Series @msc:real_analysis_notes_by_syed_gul_shah
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s$ a positive integer such that $\left| {\,{s_n}}\right|>\frac{1}{2}s$. * Theorem: Let //a// and //b// ... /t// respectively. Then (i) $\left\{a{s_n}+b{t_n}\right\}$ converges to $as+bt$. (ii) $\left\{{s_n}{t_n}\right\}$ converges to st. (iii) $\left\{\frac{{{s_n}}}{{{t_n}}} \right\}$ converges to $\frac{s}{t}$ provided ${t_n}\ne
Chapter 01 - Real Number System @msc:real_analysis_notes_by_syed_gul_shah
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(a) $\left\| {\,\underline x + \underline y \,} \right\| \le \left\| {\,\underline x \,} \right\| + \left\| {\,\underline y \,} \right\|$ (b) $\left\| {\,\underline x - \underline z \,} \right\| \le \left\| {\,\underline x - \underline y \,}
Chapter 03 - Limits and Continuity @msc:real_analysis_notes_by_syed_gul_shah
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er //s// and //t// are in $\left\{x:|x-c|<\delta \right\}$. * Theorem (Sandwiching Theorem): Suppose th... to Z$ and $h:E\to Z$ defined by $h(x)=g\left(f(x)\right)$. If //f// is continuous at $p\in E$ and if //g... rline{f}(x)=\left(f_1(x),f_2(x),f_3(x),...,f_k(x)\right)$, $x\in X$ then $\underline{f}$ is continuous on
Chapter 04 - Differentiation @msc:real_analysis_notes_by_syed_gul_shah
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uch that $\left|\underline{f}(b)-\underline{f}(a)\right|\le (b-a)\left|\underline{f'}(x)\right|$. ==== Download or View Online ==== <WRAP center round download
Topology: Short Questions and MCQs @msc:mcqs_short_questions
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he set $S=\left\{1+\frac{1}{n}: n \in \mathbb{N} \right\}$ in usual topology on $\mathbb{R}$. - What is
Syllabus for PU @msc:syllabus
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if alt="University of the Punjab Logo" class=mediaright /></html> Syllabus and scheme of studies for Reg