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3 years ago

Find the domain of the function:f (x) = 2x/x^2-4

Mathematics

1 answer:

denis23 [38]3 years ago

3 0

Answer:

see explanation

Step-by-step explanation:

The denominator of f(x) cannot be zero as this would make f(x) undefined. Equating the denominator to zero and solving gives the values that x cannot be.

x² - 4 = 0 ⇒ x² = 4 ⇒ x = ± 2 ← excluded values

domain : x ∈ R, x ≠ ± 2

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Help me please thank you

Maurinko [17]

The equation of the line with a positive slope is y≤5x-1. This eliminates choice C (third choice). From there, we can start to put the equations into slope-intercept form.

y≥3x+4
y≥-3x+4
y≥-3x-4

We see that the the equation for the second line (on the graph, not above) is y≥-3x+4. The answer is Choice 2 because both lines match its equations.

y≤5x-1 and 3x+y≥4

:)

7 0

3 years ago

Read 2 more answers

The drawing below shows a row of grocery carts that have been " nested" together. The carts are each 32in. Long. Each cart after

creativ13 [48]

Answer:

Length of Row of n cart = 11(n-1)+32 inches

The length of row for 20 nested carts will be = 11(20-1) +32 = 209 + 32 =241 inches.

Step-by-step explanation:

The length of one cart is 32 inches.

When you nest two cart, the length of the second cart will be 11 inches, so the total length of two nested cart will be 43 inches. From the this statements we can derive the following.

Length of Row of 1 cart = (1-1)*11+ 32 =32 inches

Length of Row of 2 cart =(2- 1)*11+32 = 43 inches

Length of Row of 3 cart = (3-1)*11 +32 = 54 inches

Length of Row of 4 cart = (4-1)*11 + 32 = 65 inches

Length of Row of 5 cart = (5-1)*11+32 = 76 inches

Length of Row of 6 cart = (6-1)*11+32 = 87 inches

Length of Row of 7 cart = (7-1)*11+32 = 98 inches

Length of Row of 8 cart = (8-1)*11+32 = 109 inches

Length of Row of 9 cart = (9-1)*11+32 = 120 inches

Length of Row of 10 cart = (10-1)*11+32 = 131 inches

Length of Row of n cart = (n-1)*11 + 32 =11(n-1)+32 inches

The relationship between the length of the row and the number of carts is given as Length of Row of n cart = 11(n-1)+32 inches

where n is the number of carts

The length of row for 20 nested carts will be = 11(20-1) +32 = 209 + 32 =241 inches.

4 0

3 years ago

Show all work and reasoning

Natalija [7]

Split up the interval [2, 5] into $n$ equally spaced subintervals, then consider the value of $f(x)$ at the right endpoint of each subinterval.

The length of the interval is $5-2=3$ , so the length of each subinterval would be $\dfrac3n$ . This means the first rectangle's height would be taken to be $x^2$ when $x=2+\dfrac3n$ , so that the height is $\left(2+\dfrac3n\right)^2$ , and its base would have length $\dfrac{3k}n$ . So the area under $x^2$ over the first subinterval is $\left(2+\dfrac3n\right)^2\dfrac3n$ .

Continuing in this fashion, the area under $x^2$ over the $k$ th subinterval is approximated by $\left(2+\dfrac{3k}n\right)^2\dfrac{3k}n$ , and so the Riemann approximation to the definite integral is

$\displaystyle\sum_{k=1}^n\left(2+\frac{3k}n\right)^2\frac{3k}n$

and its value is given exactly by taking $n\to\infty$ . So the answer is D (and the value of the integral is exactly 39).