Merging man & maths https://www.mathcity.org/ Thu, 04 Jun 2026 07:23:18 +0000 FeedCreator 1.8 https://www.mathcity.org/_media/logo.svg https://www.mathcity.org/ https://www.mathcity.org/fsc-part2-ptb/definitions Definitions: FSc Part 2 (Mathematics): PTB On this page, all the definitions of “Calculus and Analytic Geometry, MATHEMATICS 12” (Mathematics FSc Part 2 or HSSC-II), Punjab Textbook Board (PTB) Lahore, Pakistan are given. We are very thankful to $A=x^2$$f:X\to Y$$X$$f:X\to Y$$y$$Y$$y=ax+b$$x$$y$$f(x)=2x-6$$p(x) = {a_n}{x^n} + {a_{n - 1}}{x^{n - 1}} + {a_{n - 2}}{x^{n - 2}} + ... + {a_1}x + {a_0}$${a_0},\,{a_1},\,{a_2},...,{a_n}$$f(x)=ax+b$$X$$I:X\to X$$X$$Y$$C:X \rightarrow Y$$C(x)=a$$x \in X$$… anonymous@undisclosed.example.com (Anonymous) Sun, 20 Oct 2024 18:16:52 +0000 https://www.mathcity.org/fsc-part2-ptb/definitions-muzzammil-subhan Definitions: Mathematics 12: PTB by Muzzammil Subhan Definitions from Calculus and Analytic Geometry, MATHEMATICS 12, published by Punjab Textbook Board (PTB) Lahore, Pakistan. We are very thankful to Muzzammil Subhan for his valuable contribution. Download or view PDF for all definitions. Samples is given below$P(x)=a_0 x^0+a_1 x^1+a_2 x^2+\ldots . .+a_{n-1} x^{n-1}+a_n x^n$$n \in W$$a_0, a_1, a_2, \ldots, a_n \in R$$f(x)=a x+b$$a, b \in R$$a \neq 0$$f(x)=x$$f(x)=c$$c \in R$$\frac{P(x)}{Q(x)}$… anonymous@undisclosed.example.com (Anonymous) Sun, 20 Oct 2024 18:16:28 +0000 https://www.mathcity.org/fsc-part2-ptb/important-questions/unit-01-functions-and-limits Unit 01: Functions and Limits Here is the list of important questions. * Evaluate $\lim\limits_{\theta \to 0}\frac{1-\cos \theta}{\sin^3\theta}$ --- FBSIC (2016) * Graph the curve of the following parametric equations $x=\sec \theta$, $y=\tan\theta$ where $\theta$ is a parameter.--- FBSIC (2016) * Evaluate $\lim\limits_{x \to 2}\frac{\sqrt{x}-\sqrt{2}}{x-2}$ --- BSIC Rawalpendi(2016), BSIC Rawalpendi(2017)$f(x)=x^3+x$$\lim\limits_{\theta \to 0}\frac{\tan \theta-\sin \theta}{\sin^3\t… anonymous@undisclosed.example.com (Anonymous) Sun, 07 Feb 2021 16:47:54 +0000 https://www.mathcity.org/fsc-part2-ptb/important-questions/unit-02-differentiation Unit 02: Differentiation Here is the list of important questions. * Differentiate $\frac{(x^2+1)^2}{x^2-1}$ $w.r.t.x$. --- BSIC Gujranwala (2016) * If $x=at^2$, $y=2at$. Find $\frac{dy}{dx}$ --- BSIC Gujranwala (2016) * Differentiate $x^2-\frac{1}{x^2}$ $w.r.t.x^2$. --- BSIC Gujranwala (2016) * Prove that $\frac{d}{dx}(tan^{-1}x)=\frac{1}{1+x^2}$ --- BSIC Gujranwala (2016)$\frac{d}{dx}(sinh^{-1}x)=\frac{1}{\sqrt{1+x^2}}$$y=x^2ln(\frac{1}{x})$$\frac{dy}{dx}$$x=sin\theta$$y=sin m\t… anonymous@undisclosed.example.com (Anonymous) Sun, 07 Feb 2021 16:47:54 +0000 https://www.mathcity.org/fsc-part2-ptb/important-questions/unit-05-linear-inequalities-and-linear-programming Unit 05: Linear Inequalities and Linear Programming Here is the list of important questions. * Graph the solution region of $2x+y \geq 2$ --- BSIC Gujranwala (2016) * Graph the feasible region subject to the following constraint: --- BSIC Gujranwala (2016)$2x-3y \leq 6$$2x+3y \leq 12$$x \geq 0$$y \geq 0$$2x+y\geq 2$$x+2y\leq10$$x\geq0,y\geq0$$2x+3y\leq 12$$z=x+3y$$2x+5y\leq30$$5x+4y\leq20$$x\geq0$$y\geq0$$x+2y\leq 14$$3x+4y\leq 36$$2x+y\leq 10$$x\geq0, y\geq0$$f(x)=2x+5y$$-x\leq8$$-y\leq… anonymous@undisclosed.example.com (Anonymous) Sun, 07 Feb 2021 16:47:57 +0000