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3 years ago

Suppose f(x)=x^3+5. find the graph of f(1/3 x)

Mathematics

1 answer:

g100num [7]3 years ago

3 0

Replace x with (x/3).

Note: (x/3) = (1/3x).

f(x/3) = (x/3)^3 + 5

Using a graphing calculator, we can easily see that CHOICE 4 is the right graph.

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Please help me!!!!!!!!!!

kirill [66]

I think the answer may be D. You can graph the points and draw a line through the points to see what other points are intersected by the line.

5 0

3 years ago

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

Find the volume of the solid of revolution formed by rotating about the x--axis the region bounded by the given curves.

kherson [118]

Answer:

$=\frac{364\pi}{3}$ cubic units

Step-by-step explanation:

We are to find the volume of the solid of revolution formed by rotating about the x--axis the region bounded by the given curves.

f(x)=2x+1, y=0, x=0, x=4.

The picture is given as shaded region.

This is rotated about x axis

Limits for x are already given as 0 and 4

f(x) is a straight line

The solid formed would be a cone

Volume = $\pi \int\limits^a_b {(2x+1)^2} \, dx \\= \pi \int\limits^4_0 {(4x^2+4x+1)} \, dx \\=\pi [\frac{4x^3}{3} +2x^2+x]^5_0\\\\=\pi[\frac{4*4^3}{3}+2*4^2+4-0]\\=\frac{364\pi}{3}$

7 0

3 years ago

Please help and thx I will mark brainlest And don’t just guess Answer #4

Effectus [21]

Answer:

4. D

Step-by-step explanation:

$y=-5$ is just a graph of a constant, meaning that it has a slope of 0 and does not change.

5 0

3 years ago

Read 2 more answers

In 1990, there were 4,500 deaths due to lung diseases in miners aged 20 to 64 years. The expected number of deaths in this occup

DIA [1.3K]

Answer:

2.5

Step-by-step explanation:

We have that the standardized mortality ratio (SMR) is the relationship between the number of deaths observed in a year, that is, those that occurred and the number of expected deaths, that is, those that were predicted.

SMR = observed / expected

therefore if we replace we have:

SMR = 4500/1800

SMR = 2.5

Which means that the standardized mortality ratio (SMR) is 2.5

7 0

3 years ago