Question

Let Evaluate each of the following: f(x) = 4x, x < 5, x = 5, 10+ x, x>5.

Note: You use INF for o and-INF for -00.
(A) lim f(x)= 2-5-
(B) lim f(x)= 445+
(c) f(5)= 3

Answer 1

(A) To evaluate the limit of f(x) as x approaches 5 from the left (2-5-), we substitute values of x that are slightly smaller than 5 into the function f(x) = 4x.

lim f(x) as x approaches 5- = lim (4x) as x approaches 5-

As x approaches 5 from the left, the function becomes f(x) = 4(5) = 20.

Therefore, lim f(x) as x approaches 5- = 20.

(B) To evaluate the limit of f(x) as x approaches 5 from the right (5+), we substitute values of x that are slightly greater than 5 into the function f(x) = 10 + x.

lim f(x) as x approaches 5+ = lim (10 + x) as x approaches 5+

As x approaches 5 from the right, the function becomes f(x) = 10 + 5 = 15.

Therefore, lim f(x) as x approaches 5+ = 15.

(C) To find f(5), we substitute x = 5 into the given function f(x) = 10 + x.

f(5) = 10 + 5 = 15.

Therefore, f(5) = 15