f(x)= |x|/x for x cannot equal 0 and 0 for x=0
the value from integral -5 to 3f(x)dx is
-2?
How do I get the graph of this without using a calculator and solve for this
|x|/x = 1 for x>0
|x|/x = -1 for x<0
f(x) is just two horizontal lines, below and above the x-axis .
So, the integral from -5 to 3 is just the area of a 5x1 rectangle below the x-axis subtracted from that of a 3x1 rectangle above the x-axis.
where did you get 1 and -1 why do they equal that
recall the definition of |x|
|x| = x if x >= 0
|x| = -x if x < 0
When you divide by x, that just gives you 1 and -1
Go online to any handy graphing web site, and have it do the graph for you.
To graph the function f(x) = |x|/x, we can start by examining the behavior of the function for x > 0 and x < 0 separately.
For x > 0:
When x is positive, |x| evaluates to x. So, f(x) = |x|/x simplifies to f(x) = x/x = 1.
For x < 0:
When x is negative, |x| evaluates to -x. So, f(x) = |x|/x becomes f(x) = -x/x = -1.
At x = 0:
The function is defined as 0 since we cannot divide by 0.
Now, let's plot these values on the coordinate plane. We will have a vertical asymptote at x = 0, separating the positive and negative portions of the graph. On the positive side, the graph will be a horizontal line at y = 1. On the negative side, the graph will be another horizontal line at y = -1.
To evaluate the integral from -5 to 3 of f(x)dx, we can split the interval into two parts: from -5 to 0, and from 0 to 3.
For the interval -5 to 0, the graph is a horizontal line at y = -1. Therefore, the integral evaluates to:
∫[-5, 0] f(x)dx = ∫[-5, 0] (-1)dx = (-1)(0 - (-5)) = -5.
For the interval 0 to 3, the graph is a horizontal line at y = 1. Therefore, the integral evaluates to:
∫[0, 3] f(x)dx = ∫[0, 3] (1)dx = 1(3 - 0) = 3.
Adding the results together:
∫[-5, 3] f(x)dx = ∫[-5, 0] f(x)dx + ∫[0, 3] f(x)dx = -5 + 3 = -2.
So, the value of the integral from -5 to 3 of f(x)dx is indeed -2, as you suggested.