9514 1404 393
Answer:
x ≠ 3
Step-by-step explanation:
In any case, the domain is restricted to values of the variable for which the function is defined. The value 1/0 is not defined, so the variable cannot allow the denominator to be zero. The denominator x-3 will be zero for x=3, so that value of the variable cannot be in the domain.
The domain is all real numbers except x=3.
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<em>Additional comments</em>
It is useful to become familiar with the domains of different functions. As we saw above, the reciprocal of 0 is undefined. The square root of a negative number is undefined. The log of a non-positive number is undefined. Trig functions are defined everywhere, but their inverse functions are not. Polynomial functions are defined everywhere, but ratios of polynomials have the same restriction on denominators that we see above.
Answer:B is the answer for this question
The height of the tank must be at least 1 foot, or 12 inches. We know the floor area (which is length x width) must be at least 400 inches. Therefore these minimum dimensions already tell us that the minimum volume is 400 x 12 = 4800 cubic inches. Since we have a maximum of 5000 cubic inches, the volume must be within the range of 4800 - 5000 cubic inches.
We can set the height at exactly 1 ft (or 12 inches). Then we can select length and width that multiply to 400 square inches, for example, L = 40 inches and W = 10 in. This gives us a tank of dimensions 40 x 10 x 12 = 4800 cubic inches, which fits all the criteria.
The formula for finding circumference is Pi multiplied by diameter.
3.14 x 25ft = 78.5 feet
This would round up to 79 feet in circumference.
The table is attached in the figure.
g(x) = f(4x) ⇒⇒⇒ differentiating both sides with respect to x
∴ g'(x) = ![\frac{d}{dx} [f(x)] * \frac{d}{dx} [4x]=4*f'(x)](https://tex.z-dn.net/?f=%5Cfrac%7Bd%7D%7Bdx%7D%20%5Bf%28x%29%5D%20%2A%20%5Cfrac%7Bd%7D%7Bdx%7D%20%5B4x%5D%3D4%2Af%27%28x%29)
⇒⇒⇒⇒⇒⇒ chain role
To find g '(0.1)
Substitute with x = 0.1
from table:
f'(0.1) = 1 ⇒ from the table
∴ g'(0.1) = 4 * [ f'(0.1) ] = 4 * 1 = 4
