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scZoUnD [109]
3 years ago
12

20 points!!! is this right???

Mathematics
1 answer:
marysya [2.9K]3 years ago
3 0

Answer:

do you need help?

Step-by-step explanation:

what is the question

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If k and b are constant such that lim x approach infinity (kx+b-(x^3+1)/(x^2+1)=0. Find the values of k and b
Anna [14]

Combining the terms into one fraction, we have

kx + b - \dfrac{x^3+1}{x^2+1} = \dfrac{(k-1)x^3 + bx^2 + kx + b - 1}{x^2+1}

If this converges to 0 as x\to\infty, then the degree of the numerator must be smaller than the degree of the denominator.

To ensure this, take k=1 and b=0. This eliminates the cubic and quadratic terms in the numerator, and we do have

\displaystyle \lim_{x\to\infty} \frac{x - 1}{x^2 + 1} = \lim_{x\to\infty} \frac{\frac1x - \frac1{x^2}}{1 + \frac1{x^2}} = 0

Alternatively, we can compute the quotient and remainder of the rational expression.

\dfrac{x^3+1}{x^2+1} = x - \dfrac{x-1}{x^2+1}

Then in the limit, we have

\displaystyle \lim_{x\to\infty} \left(kx + b - x + \frac{x-1}{x^2+1}\right) = (k-1) \lim_{x\to\infty} x + b = 0

Both terms on the left vanish if k=1 and b=0.

3 0
2 years ago
Please help me solve x-6=-4x-11
labwork [276]

Answer:

<h2>-1  2/3</h2>

Step-by-step explanation:

x-6=-4x-11

+x     +x

-6=-3x-11

+11     +11

5=-3x

________

-3  -3

x=-1.66 or about -1  2/3

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Answer: change in y over Change in x(slope)

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6.4/5

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12.1/-3

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3 years ago
RIGHT<br><br><br> ACUTE<br><br><br> OBTUSE<br><br><br> EQUIANGULAR
den301095 [7]

Step-by-step explanation:

option B is correct answer ( Acute angle triangle)

hope this helps you.

4 0
3 years ago
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PLEASE HELP!!!!!!<br> WILL MARK BRAINLIEST!!!!
JulijaS [17]

Answer:

23

Step-by-step explanation:

4 0
3 years ago
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