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- Khuram Ali Khan
- Results, J. Inequal. Appl., Vol. 2010, 16 pages, (Published on October 18, 2010), Impact Factor 0.879.... . Appl., Vol. 2011, Article ID 350973, 19 pages, (Published on March 14, 2011) Impact Factor 0.73 ([[... lities and Applications, 1 (2012), No. 1, 12-32, (Published on July 9, 2012). ([[http://scik.org/index... uality for Operator Convex Functions, J. Math. Comput. Sci., vol. 2 (2012), No. 3, 656-672. ([[http://
- Question 1 and 2 Exercise 4.1 @math-11-kpk:sol:unit04
- unit of A Textbook of Mathematics for Grade XI is published by Khyber Pakhtunkhwa Textbook Board (KPTB... Given: $$a_n=\dfrac{n(n+1)}{2}$$ For first term, put $n=1,$ $$a_1=\dfrac{1(1+1)}{2}=1$$ For second term, put $n=2$. $$a_2=\dfrac{2(2+1)}{2}=3$$ For third term, put $n=3,$ $$a_3=\dfrac{3(3+1)}{2}=6$$ For forth ter
- Atiq ur Rehman, PhD
- ematics\\ COMSATS University Islamabad, Attock Campus\\ Kamra Road, Attock - PAKISTAN. </WRAP> **Ema... 4|mathscinet]] * See profile at [[http://www.scopus.com/authid/detail.url?authorId=7006197515|Scopus]] * See profile at [[http://ww2.comsats.edu.pk/fa... ractional versions of Hadamard inequalities for Caputo fractional derivatives and related results, Ope
- Computing Tools for Mathematics by Asif Arshad @notes
- ====== Computing Tools for Mathematics by Asif Arshad ====== {{ :notes:computing-tools-for-mathematics-asif-arshad.jpg?nolink|omputing Tools for Mathematics by Asif Arshad}} Computing tools for mathematics are algorithms that use co
- Question 10 Exercise 4.2 @math-11-kpk:sol:unit04
- unit of A Textbook of Mathematics for Grade XI is published by Khyber Pakhtunkhwa Textbook Board (KPTB... Peshawar, Pakistan. =====Question 10===== The population of a town is decreasing by $500$ inhabitants each year If its population in 1960 was 20135, what was its population in 1970? GOOD ====Solution==== Suppose $a_1$ represe
- Formatting Syntax @wiki
- ws Share. To remove this warning (for all users), put the following line in ''conf/lang/en/lang.php'' ... simply displays "Hello World!" to the standard output. */ class HelloWorldApp { public static void main(String[] args) { System.out.println("... pp-winapi csharp css cuesheet c_winapi dart dcl dcpu16 dcs delphi diff div dos dot d ecmascript eiffel
- Question 1 Exercise 4.5 @math-11-kpk:sol:unit04
- unit of A Textbook of Mathematics for Grade XI is published by Khyber Pakhtunkhwa Textbook Board (KPTB... ) Peshawar, Pakistan. =====Question 1(i)===== Compute the sum $3+6+12+\ldots+3.2^9$ ====Solution==== ... is the required sum. =====Question 1(ii)===== Compute the sum $8+4+2+\ldots+\dfrac{1}{16}$ ====Soluti... s the required sum. =====Question 1(iii)===== Compute the sum $2^4+2^5+2^6+\ldots+2^{10}$ ====Solutio
- FSc/ICS Part 1 (Mathematics): PTB
- >Textbook of Algebra and Trigonometry Class XI is published by Punjab Textbook Board (PTB) Lahore, Pakistan. The book has total of 14 chapters.</lead> On... Intermediate and Secondary Educations (BISE)) of Punjab and Federal Board of Intermediate and Seconda... wnloaded from the download page of [[https://pctb.punjab.gov.pk/download_books | Punjab Curriculum and
- Notes of Mathematics
- l of Complex Analysis written by Dr. M. Iqbal and published by Ilmi Kitab Khana, Lahore- PAKISTAN. The... **[[Notes:topology-and-functional-analysis-solved-pu]]**\\ Solved paper of Topology and Functional Analysis offered by the University of the Punjab, Lahore. NEW </well><well> **[[Notes:Topology... the universities this course is considered as compulsory. </well> <well> **[[Notes:Numerical-Analysi
- Definitions: FSc Part 1 (Mathematics): PTB by Aurang Zaib @fsc-part1-ptb
- *Textbook of Algebra and Trigonometry Class XI**, published by Punjab Textbook Board (PTB) Lahore, Pakistan. We are very thankful to [[:people:aurang-zaib... y operation is an operation that takes a single input and produces a single output. ===Example:=== The square root function \( \sqrt{x} \) is a unary ope
- Multiple Choice Questions (BSc/BS/PPSC) by Akhtar Abbas @notes
- viding these notes and appreciates his efforts to publish these notes on MathCity.org. Multiple Choice... these notes, which might be helpful in BSc, BS or Punjab Public Service Commission (PPSC) exams. ^ Name |Multiple Choice Questions (BSc/BS/PPSC) | ^ Aut... al part are called: - imaginary numbers - pure non real numbers - pure imaginary numbers
- Topology and Functional Analysis Solved Paper by Noman Khalid @notes
- very thankful to him for providing these notes to publish on MathCity.org. Topology and Functional An... e said subject is given for the University of the Punjab (PU), Lahore. ^ Name |Topology and Functional Analysis Solved Papers | ^ Author |Noman Khalid ... *{{ notes:topology-and-functional-analysis-solved-pu-a2011.pdf |Download PDF ~ 7.54MB}}** %%|%% <btn t
- Question 4 Exercise 4.5 @math-11-kpk:sol:unit04
- unit of A Textbook of Mathematics for Grade XI is published by Khyber Pakhtunkhwa Textbook Board (KPTB... 8}{1-0.1}=\dfrac{0.8}{0.9}=\dfrac{8}{9}$$\\ Hence putting $S_{\infty}$ in (i), we get $$0 . \overline{... ots \ldots \ldots . . . \text { (ii) }\end{align} Putting (ii) in (i), we get\\ $$1.63=1+\dfrac{7}{11}... s and given by $$S_{\infty}=\dfrac{a_1}{1-r}$$,\\ putting $a_1, r$ we get\\ $$S_{\infty}=\dfrac{0.15}{
- Question 1 and 2 Exercise 6.5 @math-11-kpk:sol:unit06
- unit of A Textbook of Mathematics for Grade XI is published by Khyber Pakhtunkhwa Textbook Board (KPTB... now by complementary events $$P(B)=1-P(\bar{B})$$ Putting \begin{align}P(\bar{B})&=\dfrac{5}{8}\\ P(B)... frac{3}{8}\end{align} Also $$P(\bar{A})=1-P(A)$$ Putting $P(A)=\dfrac{1}{2}$, we get \begin{align}P(\... now by complementary events $$P(B)=1-P(\bar{B})$$ Putting $P(\bar{B})=\dfrac{5}{8}$, we get $$P(B)=1-\
- MCQs/Objective: HSSC-I @fsc
- : Text Book of Algebra and Trigonometry Class XI (Punjab Textbook Board, Lahore) </well><well> **[[FSc... \ Text Book of Algebra and Trigonometry Class XI (Punjab Textbook Board, Lahore). </well><well> **[[FS... : Text Book of Algebra and Trigonometry Class XI (Punjab Textbook Board, Lahore). </well><well> **[[FS... ll chapters of Algebra and Trigonometry Class XI (Punjab Textbook Board, Lahore) with answers. </well