Answer:
1.B
2.common difference, d=3
Step-by-step explanation:
We are have to find the true statement about the greatest integer function
We know that the greatest integer function is defined as the value less than or equal to x.
[tex][x] means n\leq x< n+1[/tex]
A. The function is defined as the greatest integer greater than or equal to x. It is false. By above definition of greatest integer function.Option A is false
B.The greatest integer function is calssified as a piecewise function .Yes ,w ecan see that from the graph the greatest integer function is a piecewise function. Therefore, it is true.
C.The range of integer function is the set of natural numbers
It is false because the range of integer function is the set of integers.Hence, option C is false.
D. The domain of the greatest integer function is all whole number . It is false because the domain of integer function is set of real numbers not a set of whole number.Hence, option D is false.
2. We are given that a sequence
-5,-2,1,4,7,.....
[tex]a_1=-5,a_2=-2,a_3=1,a_4=4,a_5=7[/tex]
[tex]d_1=a_2-a_1=-2+5=3[/tex]
[tex]d_2=a_3-a_2=1+2=3[/tex]
[tex]d_3=a_4-a_3=4-1=3[/tex]
[tex]d_4=a_5-a_4=7-4=3[/tex]
[tex]d_1=d_2=d_3=d_4=d=3
The difference between any two consecutive terms of a sequence is equal. Hence , the sequence is AP.
The common difference of the AP is 3.
