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- Unit 02: Differentiation @fsc:fsc_part_2_solutions
- one example: We have to find the derivative of $\frac{x+1}{x-1}$ with respect to $x$. ===Method 1=== $$ \begin{aligned} \frac{d}{dx}\left(\frac{x+1}{x-1}\right) &= \frac{(x-1)\frac{d}{dx}(x+1)-(x+1)\frac{d}{dx}(x-1)}{(x-1)^2}\\ &= \frac{(x-1)(1)-(
- FSc Part 1 (KPK Boards)
- erms and to infinity of the series of the type $$\frac{a}{a(a+d)}+\frac{a}{(a+d)(a+2d)}+...$$ ===Download=== <callout type="success" icon="fa fa-download"> *... begin{smallmatrix}n\\ r\end{smallmatrix} \right)=\frac{n!}{r!(n-r)!}$, its deduction and application to ... kind of events. * recognize the formula $P(E)=\frac{n(E)}{n(S)}$, $0\leq P(E)\leq1$ for probability o
- Unit 01: Functions and Limits @fsc:fsc_part_2_solutions
- imits of Important Functions * $\lim_{x\to a}\frac{x^n-a^n}{x-a} = na^{n-1}$, where n is an integer and a>0 * $\lim_{x\to0}\frac{\sqrt{x+a} - \sqrt{a}}{x} = \frac{1}{2\sqrt{a}}$ * Limit at Infinity * Methods for Evaluating the limits at Infinity * $\lim_{x\to0}(1+\frac{1}{n})^n = e$ * $\lim_{x\to0}\frac{a^x-1}{x}
- MCQs with key @fsc:fsc_part_2_mcqs
- dratic function * (D) A cubic functions * $\frac{d}{dx} \tan 3x =$.... * (A) $3\sec^2 3x$ * (B) $\frac{1}{3}\sec^2 3x$ * (C) $\cot 3x$ * (D) $\s... (B) $dy=f'(x) dx$ * (C) $dy=f(x)$ * (D) $\frac{dy}{dx}$ * If $x<0$, $y<0$, then the point $P(x
- Chapter 13: Inverse Trigonometric Functions @fsc:fsc_part_1_solutions
- \tan ^{ - 1}}A + {\tan ^{ - 1}}B = {\tan ^{ - 1}}\frac{{A + B}}{{1 - AB}}$ * $\displaystyle{\tan ^{ - 1}}A - {\tan ^{ - 1}}B = {\tan ^{ - 1}}\frac{{A - B}}{{1 + AB}}$ ====View online or download
- Chapter 14: Solutions of Trigonometric Equation @fsc:fsc_part_1_solutions
- \tan ^{ - 1}}A + {\tan ^{ - 1}}B = {\tan ^{ - 1}}\frac{{A + B}}{{1 - AB}}$ * ${\tan ^{ - 1}}A - {\tan ^{ - 1}}B = {\tan ^{ - 1}}\frac{{A - B}}{{1 + AB}}$ ====Solutions==== <callout ty
- Chapter 01: Number System @fsc:fsc_part_1_solutions
- nd imaginary parts of (i) $(x+iy)^n$ (ii) $\left(\frac{x_1+iy_1}{x_2+iy_2}\right)^n, x_2+iy_2\neq 0$ <
- Chapter 05: Partial Fractions @fsc:fsc_part_1_solutions
- Fraction * Resolution of a Rational Fraction $\frac {P(x)}{Q(x)}$ into Partial Fractions * Exerci
- Short Questions by Mr. Akhtar Abbas @fsc:fsc_part_2_mcqs
- ous function. * Explain why the function $f(x)=\frac{2x}{x-2}$ is discontinuous at $x=2$. * Prove th