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nikklg [1K]
3 years ago
9

When the sum of 1/4 + 1/2 is divided by the product of 1/4 + 1/2 what is the quotient

Mathematics
1 answer:
zepelin [54]3 years ago
4 0
<span>When the sum of 1/4 + 1/2 is divided by the product of 1/4 + 1/2 what is the quotient </span>2
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Find lim h-&gt;0 f(9+h)-f(9)/h if f(x)=x^4 a. 23 b. -2916 c. 2916 d. 2925
Svetach [21]

\displaystyle\lim_{h\to0}\frac{f(9+h)-f(9)}h = \lim_{h\to0}\frac{(9+h)^4-9^4}h

Carry out the binomial expansion in the numerator:

(9+h)^4 = 9^4+4\times9^3h+6\times9^2h^2+4\times9h^3+h^4

Then the 9⁴ terms cancel each other, so in the limit we have

\displaystyle \lim_{h\to0}\frac{4\times9^3h+6\times9^2h^2+4\times9h^3+h^4}h

Since <em>h</em> is approaching 0, that means <em>h</em> ≠ 0, so we can cancel the common factor of <em>h</em> in both numerator and denominator:

\displaystyle \lim_{h\to0}(4\times9^3+6\times9^2h+4\times9h^2+h^3)

Then when <em>h</em> converges to 0, each remaining term containing <em>h</em> goes to 0, leaving you with

\displaystyle\lim_{h\to0}\frac{f(9+h)-f(9)}h = 4\times9^3 = \boxed{2916}

or choice C.

Alternatively, you can recognize the given limit as the derivative of <em>f(x)</em> at <em>x</em> = 9:

f'(x) = \displaystyle\lim_{h\to0}\frac{f(x+h)-f(x)}h \implies f'(9) = \lim_{h\to0}\frac{f(9+h)-f(9)}h

We have <em>f(x)</em> = <em>x</em> ⁴, so <em>f '(x)</em> = 4<em>x</em> ³, and evaluating this at <em>x</em> = 9 gives the same result, 2916.

8 0
3 years ago
729 to the power of 1 over 3
vivado [14]
So \frac{ 721^{1} }{3} ?

if so, the answer is 240\frac{1}{3}

4 0
2 years ago
Given the following values, what would the stems be? 4, 25, 56, 78, 105, 112 4 though 11 0 though 11 4 though 12 0 though 7
ss7ja [257]

Answer:

  0 though 11

Step-by-step explanation:

The stems are generally the numbers you get when you drop the units digit. The minimum number in your list is 04, so its stem would be 0. The maximum number in your list is 112, so its stem would be 11. You usually want to have the stems cover the entire range from minimum to maximum, so the stems would be 0 through 11.

___

Here's what the "stem and leaf plot" might look like for these values.

0 | 4

1 |

2 | 5

3 |

4 |

5 | 6

6 |

7 | 8

8 |

9 |

10 | 5

11 | 2

3 0
3 years ago
Kay donates twice what Ed donates.
Leviafan [203]

Answer:

ed is the independent and kay is the dependent.

Step-by-step explanation:

I dont know about the rest sorry

7 0
2 years ago
Please help! 8 and 9/20, will give brainliest. I do not tolerate spam answers! Offering triple points if you answered both!
horsena [70]

Answer:

hi, quick tip

go to cymath or just screenshot the equations or put it in, and it will automatically solve it for you instead of having to wait for someone to answer.

hope this works :}

Step-by-step explanation:

5 0
2 years ago
Read 2 more answers
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