Notes: `y = e^x, y = 2 - x^2` Use a graph to find approximate x-coordinates of the points of intersection of the given curves. Then find...

Monday, 2 December 2013

$\displaystyle{y}={{e}}^{{x}},{y}={2}-{{x}}^{{2}}$ Use a graph to find approximate x-coordinates of the points of intersection of the given curves. Then find...

$\displaystyle{y}={{e}}^{{x}},{y}={2}-{{x}}^{{2}}$

Refer the attached image. Graph of e^x is plotted in red color and graph of y=2-x^2 is plotted in blue color.

From the graph, the x-coordinates of the intersection of the curves are x $\displaystyle\approx$ -1.3 , x $\displaystyle\approx$ 0.55.

Area of the region bounded by the curves A= $\displaystyle{\int_{{-{1.3}}}^{{{0.55}}}}{\left({\left({2}-{{x}}^{{2}}\right)}-{{e}}^{{x}}\right)}{\left.{d}{x}\right.}$

$\displaystyle{A}={{\left[{2}{x}-\frac{{{x}}^{{3}}}{{3}}-{{e}}^{{x}}\right]}_{{-{1.3}}}^{{{0.55}}}}$

$\displaystyle{A}={\left[{2}{\left({0.55}\right)}-\frac{{{0.55}}^{{3}}}{{3}}-{{e}}^{{0.55}}\right]}-{\left[{2}{\left(-{1.3}\right)}-\frac{{{\left(-{1.3}\right)}}^{{3}}}{{3}}-{{e}}^{{-{1.3}}}\right]}$

$\displaystyle{A}={\left({1.1}-{0.55458333}-{1.733253018}\right)}-{\left(-{2.6}+{0.732333333}-{0.272531793}\right)}$

$\displaystyle{A}={\left(-{0.688711351}\right)}-{\left(-{2.14019846}\right)}$

$\displaystyle{A}=-{0.688711351}+{2.14019846}$

$\displaystyle{A}\approx{1.451487109}$

$\displaystyle{y}={{e}}^{{x}},{y}={2}-{{x}}^{{2}}$

Refer the attached image. Graph of e^x is plotted in red color and graph of y=2-x^2 is plotted in blue color.

From the graph, the x-coordinates of the intersection of the curves are x $\displaystyle\approx$ -1.3 , x $\displaystyle\approx$ 0.55.

Area of the region bounded by the curves A= $\displaystyle{\int_{{-{1.3}}}^{{{0.55}}}}{\left({\left({2}-{{x}}^{{2}}\right)}-{{e}}^{{x}}\right)}{\left.{d}{x}\right.}$

$\displaystyle{A}={{\left[{2}{x}-\frac{{{x}}^{{3}}}{{3}}-{{e}}^{{x}}\right]}_{{-{1.3}}}^{{{0.55}}}}$

$\displaystyle{A}={\left[{2}{\left({0.55}\right)}-\frac{{{0.55}}^{{3}}}{{3}}-{{e}}^{{0.55}}\right]}-{\left[{2}{\left(-{1.3}\right)}-\frac{{{\left(-{1.3}\right)}}^{{3}}}{{3}}-{{e}}^{{-{1.3}}}\right]}$

$\displaystyle{A}={\left({1.1}-{0.55458333}-{1.733253018}\right)}-{\left(-{2.6}+{0.732333333}-{0.272531793}\right)}$

$\displaystyle{A}={\left(-{0.688711351}\right)}-{\left(-{2.14019846}\right)}$

$\displaystyle{A}=-{0.688711351}+{2.14019846}$

$\displaystyle{A}\approx{1.451487109}$

Notes

Monday, 2 December 2013

$\displaystyle{y}={{e}}^{{x}},{y}={2}-{{x}}^{{2}}$ Use a graph to find approximate x-coordinates of the points of intersection of the given curves. Then find...

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Is there any personification in "The Tell-Tale Heart"?

Monday, 2 December 2013

Use a graph to find approximate x-coordinates of the points of intersection of the given curves. Then find...

No comments:

Post a Comment

Is there any personification in &quot;The Tell-Tale Heart&quot;?

$\displaystyle{y}={{e}}^{{x}},{y}={2}-{{x}}^{{2}}$ Use a graph to find approximate x-coordinates of the points of intersection of the given curves. Then find...

Is there any personification in "The Tell-Tale Heart"?