EASY
Mathematics
IMPORTANT
Earn 100

Prove that any function defined in a symmetrical interval can be presented as a sum of an even and an odd function. Rewrite the following functions in the form of a sum of an even and an odd function :

Important Questions on Introduction to Mathematical Analysis
EASY
Mathematics
IMPORTANT
Prove that any function defined in a symmetrical interval can be presented as a sum of an even and an odd function. Rewrite the following functions in the form of a sum of an even and an odd function : .

MEDIUM
Mathematics
IMPORTANT
Extend the function defined on the interval onto the interval in an even and an odd way.

MEDIUM
Mathematics
IMPORTANT
The function is a fractional part of a number . Prove that it is a periodic function with period

EASY
Mathematics
IMPORTANT
Sketch the graph of a periodic function with period defined on the half-open interval by the formula .

EASY
Mathematics
IMPORTANT
Let us have two periodic functions and defined on a common set. Prove that if the periods of these functions are commensurate, then their sum and product are also periodic function.

EASY
Mathematics
IMPORTANT
Prove that the Drichlet function is a periodic one but has no period.

MEDIUM
Mathematics
IMPORTANT
Prove that if the function is periodic, then is a rational number.

EASY
Mathematics
IMPORTANT
Test the following functions for monotony :
