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Suppose we take the interval [−5,7] and divide it into 4 equal subintervals. Find the width Δn of each subinterval. Δn = If we name the endpoints of the subintervals x0, x1, x2, x3 and x4 , with x0 on the left and x4 on the right, find the values of these endpoints and list them in ascending order. (Enter your answers in a comma-separated list.)

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Answer:

[tex]x_0=-5\\x_1=-2\\x_2=1\\x_3=4\\x_4=7[/tex]

Δn=3

Step-by-step explanation:

Remember, if we need to divide the interval (a,b) in n equal subinterval, then we need divide the distance (d) between the endpoints of the interval and divide it by n. Then the width Δn of each subinterval is d/n.

We have the interval [-5,7]. The distance between the endpoints of the interval is

[tex]d=7-(-5)=12[/tex].

Now, we divide d by 4 and obtain [tex]\frac{d}{4}=\frac{12}{4}=3[/tex]

Then, Δn=3.

Now, to find the endpoints of each sub-interval, we add 3 from the left end of the interval.

[tex]-5=x_0\\x_0+3=-5+3=-2=x_1\\x_1+3=1=x_2\\x_2+3=4=x_3\\x_3+3=7=x_4[/tex]

So,

[tex]x_0=-5\\x_1=-2\\x_2=1\\x_3=4\\x_4=7[/tex]

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