# Summary

• The value, a function approaches, as the variable approaches a particular value is called its limit.
• If the limit is taken by approaching the value through the values less than the given value (say a) is called left limit and if it is approached by taking values more than the given value, it is called right limit.
• Limit of a function at a point is the common value of the left and right hand limits, if they coincide.
• For a function and a real number , and may not be same (In fact, one may be defined and not the other one).
• The limits of functions f and g have the properties:
• Some standard limits to be remembered are :
• The derivative of a function f(x) at a point in defined as
• Derivative of a function at any point is defined by
• Following are some of the standard derivatives.
• The following formulae to be remembered as derivatives of standard functions:
• Geometrical meaning of is the slope (gradient) of the curve at any point
• In general stands for the rate at which changes with respect to a change in .