Question

The table shows selected values of a piecewise defined function f(x) that increases over the intervals (-∞, 3) and (3,∞). Which of the following statements are true? Select all that apply.
x y
2.7 5.4
2.8 5.6
2.9 5.8
3 ?
3.1 5.1
3.2 5.2
3.3 5.3

Which of the following STATEMENTS are true? Select all that apply.

a. limx→3+(f(x)=5)
b. limx→3-(f(x)=5)
c. limx→3+(f(x)=6)
d. limx→3-(f(x)=6)
e. limx→3(f(x)) exists because limx→3-(f(x)) and limx→3+(f(x)) are equal.
f. limx→3(f(x)) does not exist because limx→3-(f(x)) and limx→3+(f(x)) are not equal.

NOTE: the + and - symbols after the 3's are small and to the up right, like exponents.

Answer 1

Answer:

answer is a great answer (3)3) 2) 6

Answer 2

Answer:

a. True         b. True               c. False                 d. False

e. True         f. True

Step-by-step explanation:

According to the question,

The value of function f(x) increases over the interval $(-\infty,3)$ and $(3,\infty)$.

At x = 3, the value of f(x) is not defined.

a. $\lim_{x \to 3+} f(x) =5$

If x approaches to 3 from right side, then the value of f(x) tends to 5 not exactly 5. According to the given table, value of f(x) might tends to 5 over the interval $(3,\infty)$.

Thus, option (a) is true.

b. $\lim_{x \to 3-} f(x) =5$

If x approaches to 3 from left side, then the value of f(x) tends to 5 not exactly 5. According to the given table, value of f(x) might tends to 5 over the interval $(3,\infty)$.

Thus, option (b) is true.

c. $\lim_{x \to 3+} f(x) =6$

By the argument in part (a), value of function f(x) approaches to one number only. So, f(x) does not tends to 6.

Thus, option (c) is false.

d. $\lim_{x \to 3-} f(x) =6$

By the argument in part (b), value of function f(x) approaches to one number only. So, f(x) does not tends to 6.

Thus, option (d) is false.

e. The statement is true.

$\lim_{x \to 3} f(x)$ exists if and only if $\lim_{x \to 3-} f(x)$ and $\lim_{x \to 3+} f(x)$ are equal.

f. The statement is true.

$\lim_{x \to 3} f(x)$ does not exists if $\lim_{x \to 3-} f(x)$ and $\lim_{x \to 3+} f(x)$ are not equal.

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