
Find the greatest value of ,
A. -1
B. 1
C. 0
D. none of these
Answer
490.5k+ views
Hint: We first try to define the domain of the given trigonometric function. Then we state the range of the function for any values of t, . We also try to get one continuous domain of distance. At the end we find one-point x for which it attains the maximum value.
Complete step by step answer:
The main function of the given is function.
Now in a span of , it will take values of . Also, for any values of t, .
We just have to check that we can get a continuous domain of distance.
Now we find a range of . Here is the greatest integer function which means the output is the greatest integer possible less than x.
As , we can say with only integer values.
We also know for any value of x; the exponential function always gets only positive value.
So, , we can say .
So, we can see the function attains at least one continuous domain of distance as it goes towards infinity.
So, we can say the greatest value of is 1.
We can also prove it by just showing 1 value of x for which .
Let’s take .
We find the value of . So, .
So, at , . We already got a point.
So, the correct answer is “Option B”.
Note: We need to always shoe at least one point which attains the maximum point. As the part can have some fixed points due to the factor that attains only integer value. We have to show that at least one point of x satisfies the equation.
Complete step by step answer:
The main function of the given
Now in a span of
We just have to check that we can get a continuous domain of
Now we find a range of
As
We also know for any value of x; the exponential function always gets only positive value.
So,
So, we can see the function attains at least one continuous domain of
So, we can say the greatest value of
We can also prove it by just showing 1 value of x for which
Let’s take
We find the value of
So, at
So, the correct answer is “Option B”.
Note: We need to always shoe at least one point which attains the maximum point. As the part
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