All categories

3 years ago

Use the graph of the function f to determine the given limit. Picture provided below

Mathematics

2 answers:

slamgirl [31]3 years ago

7 0

Answer:

a. 2

Step-by-step explanation:

Here we have to find when lim x ---> 2, what would be the value of f(x).

The value of f(x) is nothing y value in the graph.

From the given graph, we have to see the value of y, when x = 2

The value of y = 2, when x = 2 by looking at the graph.

Therefore, the answer is a. 2

Hope you will understand the concept.

Thank you.

elena-14-01-66 [18.8K]3 years ago

6 0

Answer:

Choice B..... The limit seems to be 8

Step-by-step explanation:

From the graph, the value of the function when x approaches 2 would be 8. The point (2, 2) is an undefined point or a point of discontinuity. Therefore, the limit can not be equal to 2. Nevertheless, there is a point marked by a dark circle (2, 8). this means that when x is 2 the value of the function is 8 even though the point does not lie on the straight line.

You might be interested in

Discuss the continuity of the function on the closed interval.Function Intervalf(x) = 9 − x, x ≤ 09 + 12x, x > 0 [−4, 5]The f

quester [9]

Answer:

It is continuous since $\lim_{x\to 0^{-}} = f(0) = \lim_{x \to 0^{+} f(x)$

Step-by-step explanation:

We are given that the function is defined as follows $f(x) = 9-x, x\leq 0$ and $f(x) = 9+12x, x>0$ and we want to check the continuity in the interval [-4,5]. Note that this a piecewise function whose only critical point (that might be a candidate of a discontinuity) x=0 since at this point is where the function "changes" of definition. Note that 9-x and 9+12x are polynomials that are continous over all $\mathbb{R}$ . So F is continous in the intervals [-4,0) and (0,5]. To check if f(x) is continuous at 0, we must check that

$\lim_{x\to 0^{-}} = f(0) = \lim_{x \to 0^{+} f(x)$ (this is the definition of continuity at x=0)

Note that if x=0, then f(x) = 9-x. So, f(0)=9. On the same time, note that

$\lim_{x\to 0^{-}} f(x) = \lim_{x\to 0^{-}} 9-x = 9$ . This result is because the function 9-x is continous at x=0, so the left-hand limit is equal to the value of the function at 0.

Note that when x>0, we have that f(x) = 9+12x. In this case, we have that

$\lim_{x\to 0^{+}} f(x) = \lim_{x\to 0^{+}} 9+12x = 9$ . As before, this result is because the function 9+12x is continous at x=0, so the right-hand limit is equal to the value of the function at 0.

Thus, $\lim_{x\to 0^{-}} = f(0) = \lim_{x \to 0^{+} f(x)=9$ , so by definition, f is continuous at x=0, hence continuous over the interval [-4,5].

5 0

3 years ago

Read 2 more answers

Sofia can type the work in 10 hours. Nova can do it in 15 hours. They work together for 4 hours, then Sofia and Nova finish the

AlladinOne [14]

Answer:

2 days.

Step-by-step explanation:

Let, Sofia can type the x amount of work in 10 hours.

So, in one hour Sofia can type $\frac{x}{10}$ amount of work.

Again, Nova can type x amount of work in 15 hours.

So, in one hour Nova can type $\frac{x}{15}$ amount of work.

Hence, if they work together, they can type $\frac{x}{10} + \frac{x}{15} = \frac{6x + 4x}{60} = \frac{10x}{60} = \frac{x}{6}$ amount of work in one hour.