We have learnt the following function from our online tutor–
Constant function: y=c where c is a constant, defined for all real x.
Power function: y=x^α, where α is a positive integer. The function is defined in the infinite interval -∞<x<∞. α is a negative integer. The function is defined for all values of x except for x=0.
General exponential function: y=a^x, where a is positive not equal to unity. This function is defined for all values of x.
Logarithmic function: y=logx, a>but a is not equal to 1. This function is defined for all x>0.
Trigonometric function: y=sinx, y=cozx defined for all real x.
Y=tanx, y=secx, defined for R-(2n+1) ∏/2
Y=cotx, y=cosecx, defined for R-n∏, where n€1
It must be noted that in all these function the variable x is expresses in radians. All these functions have a very important property that is periodicity.
Limit of a function
Let y=f(x) be a function of x. If at x=a, f(x) takes indeterminate form, then we consider the values of the function which are very near to ‘a’. If these values tend to a definite unique number as x tends to ‘a’, then the unique number so obtained is called the limit of f(x) at x=a.