Continuity of function which have different definitions in different interval

Continuity of function defined differently for rational and irrational value of x

Integration of sin and cos function in different intervals

Definition & Type of Intervals

Define the continuity of a function at a point within its domain of definition. The definition of a function is given below: f(x)={{:((1-cos5x)/(x^(2))," when "(xne0)),(k," when x = 0"):} Find the value of k for which f(x) is continuous at x = 0.

Give three properties which have different magnitudes and also have different direction.

Definition Condition for continuity

Forelimb of bat and flipper of whale have different functions but indicate common ancestry.

Let f: Rto(0,1) be a continuous function. Then, which of the following function (s) has (have) the value zero at some point in the interval (0,1)?

Assertion : Sine and cosine function are perioic function Reason: sinusoidal function repear its value after a definite interval of time