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3 years ago

What is the volume of a rectangular prism

Mathematics

1 answer:

dangina [55]3 years ago

7 0

Answer:

Step-by-step explanation:

I counted all the squares

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Evaluate the limit as x approaches 0 of (1 - x^(sin(x)))/(x*log(x))

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$sin~ x \approx x ~ ~\sf{as}~~ x \rightarrow 0$

We can replace sin x with x anywhere in the limit as long as x approaches 0.

Also,

$\large \lim_{ x \to 0 } ~ x^x = 1$

I will make the assumption that log(x)=ln(x).

The limit result can be proven if the base of log(x) is 10.

$\large \lim_{x \to 0^{+}} \frac{1- x^{\sin x} }{x \log x } \\~\\ \large = \lim_{x \to 0^{+}} \frac{1- x^{\sin x} }{ \log( x^x) } \\~\\ \large = \lim_{x \to 0^{+}} \frac{1- x^{x} }{ \log( x^x) } ~~ \normalsize{\text{ substituting x for sin x } } \\~\\ \large = \frac{\lim_{x \to 0^{+}} (1) - \lim_{x \to 0^{+}} \left( x^{x}\right) }{ \log( \lim_{x \to 0^{+}}x^x) } = \frac{1-1}{\log(1)} = \frac{0}{0}$

We get the indeterminate form 0/0, so we have to use Lhopitals rule

 $\large \lim_{x \to 0^{+}} \frac{1- x^{x} }{ \log( x^x) } =_{LH} \lim_{x \to 0^{+}} \frac{0 -x^x( 1 + \log (x)) }{1 + \log (x) } \\ = \large \lim_{x \to 0^{+}} (-x^x) = \large - \lim_{x \to 0^{+}} (x^x) = -1$

Therefore,

 $\large \lim_{x \to 0^{+}} \frac{1- x^{\sin x} }{x \log x } =\boxed{ -1}$

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3 years ago

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o-na [289]

Answer

Explanation

The two lines in the diagram are secants meeting outside the circle.

The products of a secant and the extension of the chord of one line is equal to the products of a secant and the extension of the chord of the other line.

∴ 4 × 9 = x × 12

36 = 12x

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3 years ago

A business owes $8000 on a loan. Every month, the business pays 1/2 of the amount remaining on the loan. How much will the busin

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125

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3 years ago

Figure B is a scaled copy of Figure A. What is the scale factor from Figure A to Figure B?

san4es73 [151]

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Step-by-step explanation:

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3 years ago

PLEASE HELP! find the value of a in the parallelogram

Liono4ka [1.6K]

Answer:

a=19

Step-by-step explanation:

Since it is a parallelogram, adjacent angles are supplementary, or add to 180 degrees.

In this parallelogram, 5a+1 and 3a+27 are adjacent. Therefore, when added, they should equal 180.

5a+1+3a+27=180

Combine like terms

(5a+3a) + (1+27) = 180

8a +28 =180

Now, solve for a, by isolating it.

Subtract 28 from both sides

8a+28-28=180-28

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Divide both sides by 8

8a/8=152/8

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3 years ago

What is the volume of a rectangular prism​

What is the volume of a rectangular prism