This is a limit an intergral question

[tugz06]

for n is greater than or equal to 0, let fn (x)= 0, if x is less than n or x is greater than n+1
1, if x is less than or equal to n+1 and x is greater
than or equal to n

a) for each x, find the limit as n approaches infinity of f(x)

b) for each n, find the integral from -infinity to infinity of fn(x) dx

 

[Mark44]

for n is greater than or equal to 0, let fn (x)= 0, if x is less than n or x is greater than n+1
1, if x is less than or equal to n+1 and x is greater
than or equal to n

a) for each x, find the limit as n approaches infinity of f(x)

b) for each n, find the integral from -infinity to infinity of fn(x) dx

What work on this have you done? Do you have any idea what the graph of this function looks like?

 

[tugz06]

I don't know where to start for the problem and how will i obtain a graph from this problem?

 

[HallsofIvy]

The only way you will obtain the graph is by drawing it yourself! If you are working on integral equations, surely you can graph a function. Here the graph of every f_n(x) is just three horizontal straight lines.

Is it that you are having difficulty reading the definition of the f_n?

Perhaps looking at the first few will help. If n= 0, f₀(x) is 0 for x< 0, 1 for x between 0 and 1, and 0 again for x> 1.

If n= 1, f_{1[/sup](x) is 0 for x< 1, 1 for x between 1 and 2, and 0 again for x> 2.
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