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ycow [4]
3 years ago
12

Rewrite the function by completing the square. f(x) = x² +6x+87

Mathematics
1 answer:
o-na [289]3 years ago
8 0
F(x) = ( x + 3 ) ^2 + 78 is your answer.
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Find lim h->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
An adult elephant drinks about 225 liters of water each day. Is the
MissTica

Answer:

Yes, the number of days are proportional to the number of liters of water the elephant drinks.

Step-by-step explanation:

1 day: 225L  2 days: 450L  3 days: 675L  4 days: 900L

There is a proportional pattern to it.

8 0
3 years ago
I'll give brainliest!!! I need help fast please I just need someone to check my answers!!! Don't respond if you don't know what
olga2289 [7]

Answer:

your correct

Step-by-step explanation:

:D

3 0
3 years ago
Simplify y - 3 over 3 +12
Hitman42 [59]

Answer:

y-3/15

Step-by-step explanation:

5 0
2 years ago
Find the volume of the figure?l
agasfer [191]
Finding three volume is super easy the equation for volume is the area of the base times the height so u will find the area of all the small part and then add those and then multiply by the height
6 0
2 years ago
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