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denis-greek [22]
3 years ago
5

Solve for x: 4/x+4/x2-9=3/x-3

Mathematics
1 answer:
anzhelika [568]3 years ago
4 0

Answer:

x =1/12(1-√(97) )

Step-by-step explanation:

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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
Help what's is 16÷ 264
Jet001 [13]
The answer is 16 remadier 5

4 0
3 years ago
Read 2 more answers
Which best represents the solution for the inequality-100 &gt; -5y
Ira Lisetskai [31]
Y > 20

Hope this helps! Message back for an explanation:)
8 0
3 years ago
What is the simplified diffrence of the following: 150y and 100y?
Vlad [161]

Answer:

50y

Step-by-step explanation:

This is because 150 minus 100 equals 50

Also because they have the same "y" they can be subtracted easily.

7 0
3 years ago
Use the explicit formula an = a1 + (n - 1) • d to find the 350th term of the sequence below. 57, 66, 75, 84, 93, ... A. 3234 B.
mylen [45]
To use the equation we need a1 and d(the common difference).
We have a1 = 57, we need to find d.
93-84 = 9; 84-75=9; 75-66=9; 66-57=9
d = 9
a350 = 57 + (350-1)(9)
a350 = 57 + (349)(9)
a350 = 57 + 3141
a350 = 3198
4 0
3 years ago
Read 2 more answers
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