Mathematics: Find the slope and reduce. P=(2, 3) Q=(9, 7) Slope =

Find the slope and reduce. P=(2, 3) Q=(9, 7) Slope

Ответ:

viridianasar5158

22.10.2020

Mathematics

So the answer is DNC(Does Not Convergence)

Step-by-step explanation:

Given;

$\int\limits^\infty_5 {\frac{7}{x^{2}-9 } } \ dx$

We know,

The integral is an improper integral because the upper limit of integration approaches infinity. First, replace the infinite upper limit by the finite limit 'l' and take the limit of 'l' to approach infinity.

$\int\limits^\infty_5 {\frac{7}{x^{2}-9 } } \, dx=7 \lim_{l \to \infty} \int\limits^\infty_5 {\frac{1}{x^{2}-9 } } \, dx$

$7 \lim_{l \to \infty} \int\limits^\infty_5 {\frac{1}{x^{2}-3^{2} } } \, dx$

$7\times \lim_{l \to \infty} \left [ \frac{1}{2\times 3} \log\left |\frac{x-3}{x+3} \right | \right ]_{5}^{l}$ (∵We know; $\int {\frac{1}{x^{2}-a^{2} } } \, dx= \frac{1}{2\times a} \log\left |\frac{x-3}{x+3} \right |$ )

$\frac{7}{6} \times \lim_{l \to \infty} \left[ \log\left | \frac{l-3}{l+3} \right |-\log\left | \frac{5-3}{5+3}\right |\right]$

$\frac{7}{6} \times \lim_{l \to \infty} \left[ \log\left | \frac{l-3}{l+3} \right |-\log\left | \frac{-2}{8}\right |\right]$

$\frac{7}{6} \times \left[ \log\left | \frac{\infty-3}{\infty+3} \right |-\log( \frac{2}{8})\right]$ (∵ $\left | -\frac{2}{8} \right |=(\frac{2}{8} )$ )