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3 years ago

Why is it helpful to find different representations of the same number?

1 answer:

5 0

Looking at a number in different ways can help understand it’s application better. For example, giving an answer with radicals(square roots) is precise, but it’s not practical because you really don’t know what that number means.

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Use the definition to find an expression for the area under the curve y = x3 from 0 to 1 as a limit. lim n→∞ n i = 1 R (b) The f

Harlamova29_29 [7]

The summand (R?) is missing, but we can always come up with another one.

Divide the interval [0, 1] into $n$ subintervals of equal length $\dfrac{1-0}n=\dfrac1n$ :

$[0,1]=\left[0,\dfrac1n\right]\cup\left[\dfrac1n,\dfrac2n\right]\cup\cdots\cup\left[1-\dfrac1n,1\right]$

Let's consider a left-endpoint sum, so that we take values of $f(\ell_i)={\ell_i}^3$ where $\ell_i$ is given by the sequence

$\ell_i=\dfrac{i-1}n$

with $1\le i\le n$ . Then the definite integral is equal to the Riemann sum

$\displaystyle\int_0^1x^3\,\mathrm dx=\lim_{n\to\infty}\sum_{i=1}^n\left(\frac{i-1}n\right)^3\frac{1-0}n$

$=\displaystyle\lim_{n\to\infty}\frac1{n^4}\sum_{i=1}^n(i-1)^3$

$=\displaystyle\lim_{n\to\infty}\frac1{n^4}\sum_{i=0}^{n-1}i^3$

$=\displaystyle\lim_{n\to\infty}\frac{n^2(n-1)^2}{4n^4}=\boxed{\frac14}$

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3 years ago

en un circo para alimentar a 3 tigres se necesitan 40kg de carne por dia cuantos kg de carne diaria necesitaran para alimentar a

Savatey [412]

Answer:

tienes que tener 160kg de carne

Step-by-step explanation:

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2 years ago

PLZ HELP I need fine the value of x in the triangle someone plz help me

Semmy [17]

Answer: The value of X is 4 *cough*Bfb reference*cough*

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2 years ago

A company sells boxes of duck calls (d) for $35 and boxes of turkey calls (t) for $45. They make batches of duck calls that fill

natali 33 [55]

The batches that make 8 turkey calls.

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2 years ago

A student will ask his classmates one survey question. Which of the following is a statistical question that should result in va

dexar [7]

Answer:

D) What is the number of gallons of water in a pool?

Step-by-step explanation:

A statistical question consists of varied responses and not just 1 specific answer. For example, the first 3 questions only have 1 specific answer each, while the last question can vary depending on the size of the pool.

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2 years ago

Read 2 more answers