Answer:
Step-by-step explanation:
We are given that a function
We have to find the average value of function on the given interval [1,e]
Average value of function on interval [a,b] is given by
Using the formula
By Parts integration formula
u=ln x and v=dx
Apply by parts integration
By using property lne=1,ln 1=0
Answer:
The correct options are:
Option B) is never zero.
Option F) When x=0, y≠0
Step-by-step explanation:
Consider the provided function.
When we substitute x=0 in above function we get:
When we substitute x=-1 in above function we get:
When we substitute x=1 in above function we get:
The above function is exponential function which does not pass through the origin and the range of the function is a positive number.
The graph of the function is shown in figure 1.
Now consider the provided options.
Option A) is always greater than or equal to 1.
The option is incorrect as the value of the function is less than 1 for negative value of x.
Option B) is never zero
The option is correct.
Option C) When y=0, x=0
The option is incorrect.
Option D) When x=0, y=4
When x=0 the value of y is 1.
Thus, the option is incorrect.
Option E) is zero when x=0
When x=0 the value of is 1.
Thus, the option is incorrect.
Option F) When x=0, y≠0
The option is correct as 0≠1.
