Removable Discontinuity 1: Function is undefined at x = 2. However, if x 2, you

Chapter 2, Problem 25

(choose chapter or problem)

Removable Discontinuity 1: Function is undefined at x = 2. However, if x 2, you cancancel the (x 2) factors, and the equation becomesf(x) = x2 6x + 13, x 2 So f is a quadratic function with a removable discontinuity at x = 2 (Figure 2-2g). The y-value at this missing point is the limit of f(x) as x approaches 2. Figure 2-2ga. Show that f(2) has the indeterminate form0/0. What feature does the graph of f have atx = 2? Do an appropriate calculation to showthat 5 is the limit of f(x) as x approaches 2.b. Find the interval of x-values close to 2, butnot including 2, for which f(x) is within0.1 unit of 5. Keep at least six decimal placesfor the x-values at the ends of the interval.Based on your answer, what is the largestvalue of for which f(x) is within = 0.1unit of 5 when x is kept within unit of 2?c. Draw a sketch to show how the numbers L,c, , and in the definition of limit arerelated to the graph of f in this problem