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Definitions: FSc Part 2 (Mathematics): PTB
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alue //x// determines exactly one value of //y//, then we say that //y// is function of //x//. The varia... ctions. * **Logarithmic Function:** If $x=a^y$, then $y=log_ax$, where $a<0$, $a\neq 1$. * **Explici... pressed in terms of the independent variable $x$, then $y$ is called an explicit function of $x$. =====... \in D_f$ and $f'(c)=0$ or $f'(c)$ does not exists then $c$ is called critical value or point. * ** St
Unit 02: Differentiation @fsc-part2-ptb:important-questions
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// * If $x=\sin \theta, \gamma=\sin (m\theta)$, then prove that $(1-x^2)y_2-xy_1+m^2y+0$--- // BSIC Ra... --- // BSIC Rawalpindi(2017)// * If $f(x)=x^2$, then find $f'(x)$ by defination. --- // BSIC Sargodha(... If $x=\theta +\frac{1}{\theta}$ and $y=\theta +1$ then find $\frac{dy}{dx}$. --- // BSIC Sargodha(2016)/... --- // BSIC Sargodha(2016)// * If $y=e^{x^2+1}$ then find $\frac{dy}{dx}$. --- // BSIC Sargodha(2016)/
Definitions: Mathematics 12: PTB by Muzzammil Subhan
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tion:** If $y$ is easily expressed in term of $x$ then $y$ is called an explicit function. E.g. $y=x^2+3... unction:** If $y$ is not expressed in term of $x$ then $y$ is called an implicit function. E.g. $x^2+x y... ** Let $f(x)$ be a bijective function from A to B then its inverse is $f^{-1}(x)$ which is onto function... tend to a fixed number " L " as $x$ tends to $a$ then " L " is called limit of $f(x)$ as $x$ tends to $
Unit 07: Vectors @fsc-part2-ptb:important-questions
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)// * If \underlinea+\underlineb+\underlinec=0 then prove that $\underline a \times \underline b=\und... e w=-6\underline i-9 \underline j-3\underline k$, then find $|\underline u-\underline v-\underline w|$.-... nd $\cos \gamma$ are direction cosineof a vector, then prove $\cos ^2\alpha+\cos ^2\beta+\cos ^2\gamma=1
Short Term Preparation FSc 2
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ton - Lagrange - If $f(x)=\frac{x}{x^2-4}$, then domain of $f$ is - $\mathbb{R}$ - $\mathb
Unit 01: Functions and Limits @fsc-part2-ptb:important-questions
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BSIC Rawalpendi(2017)// * Evaluate $f(x)=x^2-x$ then find $f(x-1)$ --- // BSIC Gujrawala (2017)// *