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- Definitions: FSc Part 2 (Mathematics): PTB @fsc-part2-ptb
- If $c \in D_f$ and $f'(c)=0$ or $f'(c)$ does not exists then $c$ is called critical value or point. ... lled stationary point of $f$. * ** Relative maxima:** $f$ has relative maxima at $c$ if $f''(c)<0$. * ** Relative minima:** $f$ has relative manim... point is called turning point if it is either a maximum point or a minimum point. * ** Point of in
- Question 2, Exercise 9.1 @math-11-nbf:sol:unit09
- s unit of Model Textbook of Mathematics for Class XI published by National Book Foundation (NBF) as Fe... d, Pakistan. =====Question 2(i)===== Find the maximum and minimum values of the reciprocal trigonome... orname{Sin}} \theta\leq 1 \\ \end{align*} Hence maximum value $(M) = 1$ \\ and minimum value $(m) = \d... {1}{7}$. GOOD =====Question 2(ii)===== Find the maximum and minimum values of the reciprocal trigonome
- Real Analysis: Short Questions and MCQs @msc:mcqs_short_questions
- rational numbers? - Is there a rational number exists between any two rational numbers. - Is there a real number exists between any two real numbers. - Is the set o... nel><panel> 5. Concept of the divisibility only exists in set of .............. * (A) natural num... > 8. A set $A$ is said to be countable if there exists a function $f:A\to \mathbb{N}$ such that *
- Question 1, Exercise 9.1 @math-11-nbf:sol:unit09
- s unit of Model Textbook of Mathematics for Class XI published by National Book Foundation (NBF) as Fe... Pakistan. =====Question 1(i)===== Find the maximum and minimum values of the trigonometric functi... orname{Cos} \theta \leq 4 \\ \end{align*} Hence maximum value $(M) = 4$ \\ and minimum value $(m) = 0$... ients: $$a=2, \quad b=-2$$ \begin{align*} \text{Maximum value (M)} & = a+|b|\\ & = 2+|-2| \\ & = 2+2 =
- Unit 08: Fundamental of Trigonometry @math-11-nbf:sol
- the book "Model Textbook of Mathematics for Class XI" published by National Book Foundation (NBF) as F... * [[math-11-nbf:sol:unit08:ex8-2-p9|Question 8(x, xi & xii) ]] * [[math-11-nbf:sol:unit08:ex8-2-p10|Question 8(xiii, xiv & xv) ]] * [[math-11-nbf:sol:unit08:ex8-
- Khuram Ali Khan
- ara Nosheen and Josip Pečarić, n-exponential Convexity of some dynamic Hardy-type functionals, Journal... [http://jmi.ele-math.com/08-24/n-exponential-convexity-of-some-dynamic-Hardy-type-functionals|Link]]) ... w/journals/math/18/1/article-p632.xml|Link]]) - Xiaoli Qiang, Ghulam Farid, Muhammad Yussouf, Khuram... espect to another Function and Application, Complexity, 2021 Article ID 9260828 (Published September 0
- MTH321: Real Analysis I (Spring 2023) @atiq
- o $s$. - For each irrational number $x$, there exists a sequence $\left\{ {{r}_{n}} \right\}$ of dis... y if for any real number $\varepsilon >0$, there exists a positive integer ${{n}_{0}}$ such that $\lef... op{\lim }}\,f(x)$, where $p\in [0,1]$ does not exist. - If $\underset{x\to c}{\mathop{\lim }}\,f(x)$ exists, then it is unique. - A function $f(x)={{x}^
- Question 8(xix, xx, xxi & xxii) Exercise 8.2 @math-11-nbf:sol:unit08
- ====== Question 8(xix, xx, xxi & xxii) Exercise 8.2 ====== Solutions of Question 8(xix, xx, xxi & xxii) of Exercise 8.2 of Unit 08: Funda
- Question 3(xi, xii & xiii) Exercise 8.3 @math-11-nbf:sol:unit08
- ====== Question 3(xi, xii & xiii) Exercise 8.3 ====== Solutions of Question 3(xi, xii & xiii) of Exercise 8.3 of Unit 08: Fundamenta
- MTH322: Real Analysis II (Spring 2023) @atiq
- ty }{f(x)\,dx}$ converges if, and only if, there exists a constant $M>0$ such tha $\int\limits_{a}^{b}... y $b\ge a$ and for every $\varepsilon >0\,$there exists a $B>0\,$ such that \[\left| \,\int_{b}^{c}{f... y $\varepsilon>0$ and for all $x\in[a,b]$, there exist an integer $N$ such that $$\left|f_{n+p}(x)-f_n... e uniformly (and absolutely) on $[a,b]$ if there exists a convergent series $\sum M_n$ of positive num
- Definitions: FSc Part 1 (Mathematics): PTB by Aurang Zaib @fsc-part1-ptb
- from **Textbook of Algebra and Trigonometry Class XI**, published by Punjab Textbook Board (PTB) Lahor... ystem, the real plane consists of a horizontal x-axis and a vertical y-axis. Any point in this plane can be represented by an ordered pair \( (x, y) \), w... artesian coordinate system, where the horizontal axis represents the real part, and the vertical axis
- MCQs or Short Questions @atiq:sp15-mth321
- ne of these - Concept of the divisibility only exists in set of .............. * (A) natural num... t{3}$ * (D) 7 - Is there a rational number exists between any two rational numbers. - Is there a real number exists between any two real numbers. - Is the set o... ? - A set $A$ is said to be countable if there exists a function $f:A\to \mathbb{N}$ such that *
- Question 8(x, xi & xii) Exercise 8.2 @math-11-nbf:sol:unit08
- ====== Question 8(x, xi & xii) Exercise 8.2 ====== Solutions of Question 8(x, xi & xii) of Exercise 8.2 of Unit 08: Fundamental of Trigonometry. This is unit of Model Textbook of Mat
- Question 8(xiii, xiv & xv) Exercise 8.2 @math-11-nbf:sol:unit08
- ====== Question 8(xiii, xiv & xv) Exercise 8.2 ====== Solutions of Question 8(xiii, xiv & xv) of Exercise 8.2 of Unit 08: Fundamental of Trigonometry. This is unit of Model Textbook
- Atiq ur Rehman, PhD
- Hermite-Hadamard Type Inequalities For (h−m)−Convexity, Electron J. Math. Anal. Appl. 6(2) (2018), 31... J. Pečarić , Atiq Ur Rehman, On Logarithmic Convexity for Giaccardi's Difference, Rad HAZU 515 (2013)... utt, J. Pečarić, Atiq ur Rehman, Exponential convexity for Petrović and related functionals, J. Inequa... . J. Pečarić, Atiq ur Rehman, On Exponential Convexity for Power Sums and Related Results, J. Math. I
- Recent Advances in Mathematical Methods, Models & Applications, LSC Lahore, Pakistan (April 13-14, 2019) @conferences
- Syllabus & Paper Pattern for General Mathematics (Split Program) @bsc:paper_pattern:punjab_university
- Symposium on “Computational Complexities, Innovations and Solutions (CCIS)", COMSATS, Abbottabad (10 - 11 May 2010) @conferences
- Chapter 12: Graph of Trigonometric and Inverse Trigonometric Functions and Solutions of Trigonometric Equations @fsc:kpk_fsc_part_1
- Ch 07: Permutation, Combination and Probability: Mathematics FSc Part 1 @fsc:fsc_part_1_solutions:ch07