EASY
Mathematics
IMPORTANT
Earn 100

Prove that any function fx defined in a symmetrical interval -l, l 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 : fx=x+21+x2

Important Questions on Introduction to Mathematical Analysis

EASY
Mathematics
IMPORTANT

Prove that any function fx defined in a symmetrical interval -l, l 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 : y=ax.

MEDIUM
Mathematics
IMPORTANT
Extend the function fx=x2+x defined on the interval 0,3 onto the interval -3,3 in an even and an odd way.
MEDIUM
Mathematics
IMPORTANT
The function x=x-Ex is a fractional part of a number x. Prove that it is a periodic function with period 1.
EASY
Mathematics
IMPORTANT
Sketch the graph of a periodic function with period T=1 defined on the half-open interval 0,1 by the formula y=x2.
EASY
Mathematics
IMPORTANT
Let us have two periodic functions fx and φx 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 λx is a periodic one but has no period.
MEDIUM
Mathematics
IMPORTANT
Prove that if the function fx=sinx+cospx is periodic, then p is a rational number.
EASY
Mathematics
IMPORTANT
Test the following functions for monotony : fx=x