Exercise 1. Assume f : [a, b] ! R is integrable. (a) Show that if g satisfies g(x) = f(x) for all but a finite number of points in [a, b], then g is integrable as well. What is the integral of g? (b) Find an example to show that g may fail to be integrable if it di↵ers from f at a countable number of points.

Step-by-step explanation:

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step-by-step explanation:

answer: the price of one pound cabbage = $ 0.8

the point (10,8) represents that the cost of 10 pounds cabbage is $ 8

step-by-step explanation:

since, here is a proportional relation between the number of pounds of cabbage (x) and the price in dollars (y).

therefore, we can write,

⇒ y = k x

where k is the constant of proportionality.

now, point (5,4) is in the line.

thus, it will satisfies the above equation of line.

⇒ 4 = 5 k

⇒ k = 0.8

thus, the equation of the line is,

y = 0.8 x

a) for x = 1,

y = 0.8

therefore, the cost of one pound of cabbage is 0.8 dollars.

b) in the below graph (10,8) represents that the cost of 10 pounds of cabbage is 8 dollars.