1. When does limit exists?
= Limit exists in the following condition:
Left hand limit and right hand limit both exists
Left hand limit = Right hand limit
2. What is an indeterminant form?
= It is an expression involving two function whose limit cannot be determined solely
from the limit of the individual function.
Example: 0/0, ∞/∞, 0*∞, ∞-∞, 1^∞
3. When is a function called continuous?
= A function is called continuous if:
Functional value exists
Left hand limit and right hand limit exists
Left hand limit = Functional value = Right hand limit
4. How do we solve the problem if instantaneous rate of change?
= It is the change in the rate at a particular instant and it’s same as the change in the
derivatives value at a specific point.
Formula = dP/dt
5. What is an implicit function?
= A mathematical function defined by mean of relation that is not solved for the
function in term of the independent variable or variables.
6. What is average and marginal cost?
= Average Cost:
If the total cost is divided by total quantity produced, it is called average cost.
AC = C(q)/q
Marginal Cost:
The addition in total cost as a result of increase in production of output by one more
unit is called marginal cost.
MC = d/dq [C(q)]
7. At what condition is a function maximum and minimum?
= The condition for maximum function:
i. f’(x)=0
ii. f”(x)<0
The condition for minimum function:
i. f’(x)=0
ii. f”(x)>0
8. What is function increasing or decreasing?
= If f’(x) > 0 on an open interval the function is increasing
If f’(x) < 0 on an open interval then function is decreasing.
9. When is a demand elastic, inelastic or unit elastic?
= If elasticity is less than 1 it is elastic
dR/dp < 0
nd > 1
If elasticity is greater than it is inelastic
dR/dp > 0
nd < 1
If elasticity is equal to 1 it is unit elastic
dR/dp = 0
nd = 1
10. What happens to revenue when price is elastic?
= When the price is elastic then, the rate change of revenue dR/dp < 0, with respect to
the price is negative.
i.e. increase in price result the decrease in revenue and decrease in price results the
increase in revenue.
11. Formula for elasticity of demand and supply?
= Elasticity of demand
nd = -p/q * dq/dp
Elasticity of supply
nd = p/q * dq/dp
12. What is the profit maximizing condition in a monopolistic firm?
= The profit maximizing condition of monopolistic firm are:
MR = MC and MR’ < MC’
13. What is the profit maximizing condition in a perfect competitive firm?
= The profit maximizing condition in a perfect competitive firm are:
MR = P = AR
MR = MC
MC’ > 0
14. What is a Cobb- Douglas Production Function?
= The Cobb- Douglas production function represents the relationship between two or
more inputs typically physical capital and labour and the number of output that can be
produced.
Relationship of an output to input.
Q (L,K) = bL^αK^β
15. Define Euler’s Theorem for Homogeneous Function?
= Let u = f(x,y) be a homogenous function of degree n in two independent variables x &
y then,
X du/dx + y du/dy = nu.
16. Give the formula for total derivative of three variables
= du/dt = Ux dx/dt + Uy dy/dt + Uz dz/dt
OR,
dU = Uxdx + Uydy + Uzdz
17. How do we find error of percentage using derivatives?
= We’ll devide the error by the total amount and multiply by 100.
18. What condition is called a saddle point?
= A critical point that is neither a relative maximum nor a relative minimum is called a
saddle point.
(x,y) = (a,b)
If,
D = Uxx Uyy – (Uxy)^2 < 0
19. What are Langrange multiplier?
= In mathematical optimization, the method of langrange multiplier is a strategy for
finding the local maxima and minima of a function subject to equality constraints.
L(x,y,z,λ) = f(x,y,z) = λØ(x,y,z)
20. What is the integration of e^4x?
= e^4x
Ѕe^4x dx
Let u = 4x
Then
du/dx = 4
dx = du/4
Se^4x dx = Se^4 du/4
= ¼ Se^4 du
Se^4x dx = ¼ e^4x + c
21. When is an integral called an improper integral?
= Improper integral are definite integral where one or both of the boundaries is at
infinity.
22. When is an improper limit called convergent or divergent?
= When the integration of the improper limit exists, then it is called convergent.
When the integration of the improper limits doesn’t exists, then it is called divergent.
23. What is a differential equation?
= An equation that relates one or more function and their derivatives is called a
differential equation.
A mathematical equation for an unknown function of one or several variables that
relates the value of the function itself to its derivatives of various order.
24. What is an open half plane region?
= A half plane is a planer region consisting of all points on one side of an infinite straight
line and no points on the other side.
If the points on the line are not included then it is called open half plane region.
25. What is Linear Programming?
= Linear programming is a mathematical technique used in decision making process for
optimization of the objective function subject to given constraints, assuming that the
relation between variable be linear.
26. What is the derivative of logx?
= d/dx (logx) = 1/x
27. What is consumer surplus? Give its formula
= Consumer surplus is the difference between the price that a consumer eager to pay
and what he actually pays for a commodity.
Consumer’s surplus = xₒᶺꚂᵥₒ f(x) dx – pₒ xₒ
Where, nₒ → quantity purchased
pₒ → price
28. What is producer’s surplus? Give its formula
= Producer’s surplus is the difference between total revenue actually received and total
revenue he would have been willing to receive.
Producer’s surplus = pₒxₒ - xₒᶺꚂᵥₒ g(x) dx
29. What is a Unique Optimal solution?
= The solution which occurs at only one vertex is called unique optimal solution
30. Explain Integration by parts. What is the priority for order for assumption of u.
= Integration by parts is a process that finds the integral of a product of functions in
terms of the integral of the product of their derivative and antiderivative.
The priority order for the assumption of u is
- Logarithmic, algebraic, trigonometric & exponential
(LATE)
Ꚃuvdx = uꚂvdx - Ꚃ{dy/dx Ꚃvdx} dx
Define limit of a function.
= Limit of a function is a fundamental concept in a calculus and analysis concerning
the behavior of that function near a particular input.
