Given
\(x=\frac{100}{P}=100P^{-1}\)
\(\therefore \frac{dx}{dp}=100(-1)P^{-1-1}\)
= 100(-1)P^-2
= -100(P^-2)
= \(\frac{-100}{p^2}\)
At P = 2,
\(\frac{dx}{dp}=\frac{-100}{4}=-25\) and \(x=\frac{100}{2}=50\)
Substituting the values in formula
\(e_{d}=\frac{Pdx}{xdp}=\left ( \frac{2}{50} \right )\left ( \frac{-100}{4} \right )=\frac{-200}{200}=-1\)
e_d = -1

Given that TC(Q) = 192 + 48Q + 4Q²
(i) MC (Q) = \(\frac { d(TC(Q)) }{ dQ } \) = 0 + 48 + 8Q
MC = 48 + 8Q
(ii) Average Cost =\(\frac { TC(Q) }{ dQ } =\frac { 192+48Q+4Q^{ 2 } }{ Q } \)
Average Cost = \(\frac { 192 }{ Q } \) + 48 + 4Q
(iii) Fixed Cost = Value of the constant = 192
(iv) Average Fixed Cost = \(\frac { 192 }{ Q } \)
(v) Average Variable Cost =\(\frac { TVCQ }{ Q } \)
TVC(Q) = TCQ - Constant
= 48Q + 4Q²
∴ AVC =\(\frac { 48Q+4Q^{ 2 } }{ Q } \)= 48 + 4Q

The coefficient and the constant terms are given below for the equations
\(\triangle =\left| \begin{matrix} 2 & 3 \\ 2 & 1 \end{matrix} \right| \)
\(\triangle =2-6=-4\)
\(\triangle { x }_{ 1 }=\left| \begin{matrix} 7 & 3 \\ 5 & 1 \end{matrix} \right| \)
\(=7-15=-8\)
\( \triangle { x }_{ 2 }=\left| \begin{matrix} 2 & 7 \\ 2 & 5 \end{matrix} \right| \)
\(=10-14=-4\)
\(By\quad Carmer's\quad rule\)
\( { x }_{ 1 }=\frac { \triangle { x }_{ 1 } }{ \triangle } \)
\(=\frac { -8 }{ -4 } \)
\(=2\)
\({ x }_{ 2 }=\frac { \triangle { x }_{ 2 } }{ \triangle } \)
\(=\frac { -4 }{ -4 } =1\)
\(solution\quad set\)
\(\left( { x }_{ 1 }{ ,x }_{ 2 } \right) =\left\{ 2,1 \right\} \)

Differential calculus measures the rate of change of functions. In Economics it is also necessary to reverse the process of differentiation and find the function F(x) whose rate of change has been given. This is called integration. The function F(x) is termed an integral or anti-derivative of the function f(x) The integral of a function f(x) is expressed mathematically as \(\int { f\left( x \right) dx } =F(x)+C\)
Here the left hand side of the equation is read "the integral of f(x) with respect to x" The symbol +" is an integral sign, f(x) is integrand, C is the constant of integration, and F(x)+c is an indefinite integral. It is so called because, as a function of x, which is here unspecified, it can assume many values.

a) Click Start Menu
b) Click Program
c) Select Microsoft Power Point - Click.
d) New Power Point file will open, and then type the title and subtitle if wanted.
g) A new slide can be inserted by 'Click' on icon 'New slide' or using short key 'Crtl + M'
h) We can type content, insert the table, picture, movies, sounds, etc., with the content.
i) Tab 'Design' helps to design the slide (can select common from the first slide or separate slide for each slide)
j) Click icon slide show, one can run slide show either starting from the first slide or starting from the current slide.