1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
tino4ka555 [31]
3 years ago
15

I already answered this but I just want to make sure if I did it right

Mathematics
1 answer:
galben [10]3 years ago
6 0
\bf \left( \cfrac{2}{3} \right)^3\cdot \left( \cfrac{3}{5} \right)^3\implies \cfrac{2^3}{\underline{3^3}}\cdot \cfrac{\underline{3^3}}{5^3}\implies \cfrac{2^3}{5^3}\implies \cfrac{8}{125}
You might be interested in
How do you find the limit?
coldgirl [10]

Answer:

2/5

Step-by-step explanation:

Hi! Whenever you find a limit, you first directly substitute x = 5 in.

\displaystyle \large{ \lim_{x \to 5} \frac{x^2-6x+5}{x^2-25}}\\

\displaystyle \large{ \lim_{x \to 5} \frac{5^2-6(5)+5}{5^2-25}}\\

\displaystyle \large{ \lim_{x \to 5} \frac{25-30+5}{25-25}}\\

\displaystyle \large{ \lim_{x \to 5} \frac{0}{0}}

Hm, looks like we got 0/0 after directly substitution. 0/0 is one of indeterminate form so we have to use another method to evaluate the limit since direct substitution does not work.

For a polynomial or fractional function, to evaluate a limit with another method if direct substitution does not work, you can do by using factorization method. Simply factor the expression of both denominator and numerator then cancel the same expression.

From x²-6x+5, you can factor as (x-5)(x-1) because -5-1 = -6 which is middle term and (-5)(-1) = 5 which is the last term.

From x²-25, you can factor as (x+5)(x-5) via differences of two squares.

After factoring the expressions, we get a new Limit.

\displaystyle \large{ \lim_{x\to 5}\frac{(x-5)(x-1)}{(x-5)(x+5)}}

We can cancel x-5.

\displaystyle \large{ \lim_{x\to 5}\frac{x-1}{x+5}}

Then directly substitute x = 5 in.

\displaystyle \large{ \lim_{x\to 5}\frac{5-1}{5+5}}\\

\displaystyle \large{ \lim_{x\to 5}\frac{4}{10}}\\

\displaystyle \large{ \lim_{x\to 5}\frac{2}{5}=\frac{2}{5}}

Therefore, the limit value is 2/5.

L’Hopital Method

I wouldn’t recommend using this method since it’s <em>too easy</em> but only if you know the differentiation. You can use this method with a limit that’s evaluated to indeterminate form. Most people use this method when the limit method is too long or hard such as Trigonometric limits or Transcendental function limits.

The method is basically to differentiate both denominator and numerator, do not confuse this with quotient rules.

So from the given function:

\displaystyle \large{ \lim_{x \to 5} \frac{x^2-6x+5}{x^2-25}}

Differentiate numerator and denominator, apply power rules.

<u>Differential</u> (Power Rules)

\displaystyle \large{y = ax^n \longrightarrow y\prime= nax^{n-1}

<u>Differentiation</u> (Property of Addition/Subtraction)

\displaystyle \large{y = f(x)+g(x) \longrightarrow y\prime = f\prime (x) + g\prime (x)}

Hence from the expressions,

\displaystyle \large{ \lim_{x \to 5} \frac{\frac{d}{dx}(x^2-6x+5)}{\frac{d}{dx}(x^2-25)}}\\&#10;&#10;\displaystyle \large{ \lim_{x \to 5} \frac{\frac{d}{dx}(x^2)-\frac{d}{dx}(6x)+\frac{d}{dx}(5)}{\frac{d}{dx}(x^2)-\frac{d}{dx}(25)}}

<u>Differential</u> (Constant)

\displaystyle \large{y = c \longrightarrow y\prime = 0 \ \ \ \ \sf{(c\ \  is \ \ a \ \ constant.)}}

Therefore,

\displaystyle \large{ \lim_{x \to 5} \frac{2x-6}{2x}}\\&#10;&#10;\displaystyle \large{ \lim_{x \to 5} \frac{2(x-3)}{2x}}\\&#10;&#10;\displaystyle \large{ \lim_{x \to 5} \frac{x-3}{x}}

Now we can substitute x = 5 in.

\displaystyle \large{ \lim_{x \to 5} \frac{5-3}{5}}\\&#10;&#10;\displaystyle \large{ \lim_{x \to 5} \frac{2}{5}}=\frac{2}{5}

Thus, the limit value is 2/5 same as the first method.

Notes:

  • If you still get an indeterminate form 0/0 as example after using l’hopital rules, you have to differentiate until you don’t get indeterminate form.
8 0
3 years ago
What number is 10,000 less than 337,676?
podryga [215]
327.676 is the answer u just have to subtract
6 0
3 years ago
Read 2 more answers
What’s this I don’t know
avanturin [10]

Answer:

C.

Step-by-step explanation:

its C.

7 0
2 years ago
One serving of this cereal provides you with 160 mg of sodium. This is 7% of your body's daily needs. How many milligrams of sod
denis23 [38]
First, we see the closest multiple of 7 under 100 is 98 and that divided by 7 is 14. there are 2/7 as our remainder. We do 2/7 times 160 to get 320/7 and 320/7 = 45 and 5/7. We convert 5/7 into a decimal like 5/7 = .7. The answer is 45.7 milligrams of sodium.
6 0
3 years ago
YES I AM GIVING A BRAINLIST :D
zhuklara [117]

Answer:

y=10x-2x ................

3 0
2 years ago
Other questions:
  • Compare the two functions give. explain which function has the greater rate of change
    11·1 answer
  • PLSSSS HELPP ASSPPPP!!!!
    15·1 answer
  • (b) we often read that iq scores for large populations are centered at 100. what percent of these 78 students have scores above
    15·1 answer
  • A group of 75 math students were asked whether they like algebra and whether they like geometry. A total of 45 students like alg
    9·2 answers
  • How many hours are in 8:15 to 12:45
    7·2 answers
  • Find the slope of the line
    12·1 answer
  • How are u alive plss hlp<br><br> .
    7·1 answer
  • A basketball team had four players tryout for each of the five positions. How many ways could the team be formed?
    10·1 answer
  • ANSWER FOR BRAINLIEST
    15·2 answers
  • LOOKING FOR COCO!!! COCO WHERE R U???
    10·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!