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nadezda [96]
3 years ago
15

The answers to the 3 questions

Mathematics
1 answer:
Simora [160]3 years ago
3 0
  • It is linear as the equation performs ax+by +c
  • y = 90.2x - 177670
  • number of student to enroll 2011 is 3722

Step-by-step explanation:

  • Linear is a straight line.
  • Quadratic is a square which generates parabola.
  • Quadratic formula is (ax)^2 + bx + c = 0.
  • Linear formula is ax+bx + c = 0
  • To  forecast time series data modelling can be used.
  • To form a linear equation y = mx + c.
  • After finding x is the required value , m is the intercept and C constant.
  • X axis have years and Y axis has the value.
  • to find number of students x is 90.2 * 2011 - 177670.
  • The result comes to 3722.
  • In Data analysis predictive modeling is the second phase.
  • It is important because it helps in associating to variables.
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SOLUTION We observe that f '(x) = -1 / (1 + x2) and find the required series by integrating the power series for -1 / (1 + x2).
Ann [662]

Answer:

Required series is:

\int{\frac{-1}{1+x^{2}} \, dx =-x+\frac{x^{3}}{3}-\frac{x^{5}}{5}+\frac{x^{7}}{7}+.....

Step-by-step explanation:

Given that

                           f'(x) = -\frac{1}{1 + x^{2}} ---(1)

We know that:

                  \frac{d}{dx}(tan^{-1}x)=\frac{1}{1+x^{2}} ---(2)

Comparing (1) and (2)

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Using power series expansion for tan^{-1}x

f'(x)=-tan^{-1}x=-\int {\frac{1}{1+x^{2}} \, dx

= -\int{ \sum\limits^{ \infty}_{n=0} (-1)^{n}x^{2n}} \, dx

= -\sum{ \int\limits^{ \infty}_{n=0} (-1)^{n}x^{2n}} \, dx

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=C+\sum\limits^{ \infty}_{n=0} (-1)^{n+1}\frac{x^{2n+1}}{2n+1}

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as

                 tan^{-1}(0)=0 \implies C=0

Hence,

\int{\frac{-1}{1+x^{2}} \, dx =-x+\frac{x^{3}}{3}-\frac{x^{5}}{5}+\frac{x^{7}}{7}+.....

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