Class 11th mathematics (limits and derivatives)

-

What are Limits?

l is called limit of the function f(x) if the equation is given as x → a, f(x) → l, and this is symbolically written for all the limits, the function should assume at a given point x = a. x could approach a number in two ways, either from the left or from the right, i.e., all the values of x near a could be greater than a or could be less thana.

What is Right-Hand Value?

In this type of limits, Right-hand limit Value is referred to the situation in which f(x) gets dictated by values of f(x) when x tends to from the right.

What is Left-Hand Value?

In the case of Left-hand limit, when x tends to from the left, the value of f(x) gets dictated by values of f(x).
In this case, the right and left-hand limits are different, and hence we say that the limit of f(x) as x tends to zero does not exist (even though the function is defined at 0). This could also be followed in limits and continuity of values.

Standards In Limits

The given are some limit’s standards:
  • limx→axn−an/x−a=nan−1
  • limx→0sinx/x=1
  • limx→01−cosx/x=0

Derivative of the Function

If we are referring to a function f at a, then it’s equation is defined by
f′(a)=limh→0f(a+h)−f(a)/h
Similarly the derivation of a function f at x is :
f′(x)=df(x)/dx=limh→0f(x+h)−f(x)/h

Standards In Derivatives

The given are some derivative’s standards:
  • d/dx(xn)=nxn−1
  • d/dx(sinx)=cosx
  • d/dx(cosx)=-sinx
  • d/dx(cosx)=−sinx8

Comments

Post a Comment

Popular posts from this blog

Class 11th science chemistry (thermodynamics)

-
Image
Thermodynamics deals with the change of energy in physical and chemical processes. It allows us to study these changes quantitatively as well as to make effective predictions. Therefore, we divide the universe as surrounding and system. Physical or chemical processes lead to progression or immersion of heat part of it may be converted to work. According to the first law of thermodynamics , these quantities are related as ∆U = q + w where q is heat and w is work. Change in internal energy is a state function and depends on only the initial and final states. On the other hand, w and q are not state functions. The change in temperature due to the transfer of heat one system to another system can be measured. Heat evolved or absorbed is expressed as q = C∆T. In case of expansion of gas, work is measured as w = –p ex ∆V Enthalpy Change Enthalpy change is defined as the change in energy of a system at constant pressure. It is denoted as ΔH. Enthalpy is a state function. Enthalpy ch...
Read more

Class 11th science chemistry (Redox reaction)

-
Image
Redox reaction is the combination of both oxidation and reduction reactions. When redox reaction takes place, both oxidation and reduction reactions also occur simultaneously. What is a Redox Reaction? Redox is a term used for the oxidation-reduction reaction. Redox reaction is a chemical reaction where a change in the oxidation state of atoms occurs. It involves electron transfer i.e if one chemical species gains electrons, then another chemical species gives or loses electrons. The species from which the electron is lost is said to be oxidized whereas the species to which the electron is added is said to be reduced. Example zinc displaces copper in an aqueous solution called copper sulfate. Redox reactions can be classified into four different categories: Combination reaction Decomposition reaction Displacement reaction Disproportionation reaction Oxidizing And Reducing Agents The role of an oxidizing agent (Oxidant) in a chemical reaction is to gain electrons. ...
Read more