Notes: Problem in solving an indeterminate limit [0/0] `lim_(x->0) (sin^2 x)/(1-2sin((5pi)/6 - x)cos x) ` Because I find it easier to solve it if I switch...

Saturday, 5 July 2014

Problem in solving an indeterminate limit [0/0] $\displaystyle\lim_{{{x}\to{0}}}\frac{{{{\sin}}^{{2}}{x}}}{{{1}-{2}{\sin{{\left(\frac{{{5}\pi}}{{6}}-{x}\right)}}}{\cos{{x}}}}}$ Because I find it easier to solve it if I switch...

You need
to evaluate the following limit such that:

$\displaystyle\lim_{{{x}\to{0}}}{\left({{\sin}}^{{2}}\right.}$
x)/(1-2sin((5pi)/6 - x)cos x) = (sin^2 0)/(1 - 2sin((5pi)/6)*cos 0)

Since
$\displaystyle{\sin{{0}}}={0}$ and $\displaystyle{\cos{{0}}}={1}$ yields:

$\displaystyle\lim_{{{x}\to{0}}}{\left({{\sin}}^{{2}}\right.}$
x)/(1-2sin((5pi)/6 - x)cos x) = 0/(1 - 2sin((5pi)/6))

You need to evaluate
$\displaystyle{\sin{{\left(\frac{{{5}\pi}}{{6}}\right)}}}={\sin{{\left(\frac{\pi}{{3}}+\frac{\pi}{{2}}\right)}}}$

Using the identity $\displaystyle{\sin{{\left({a}+{b}\right)}}}={\sin{{a}}}\cdot{\cos{{b}}}$
+ sin b*cos a $\displaystyle{y}{i}{e}{l}{d}{s}:$

$\displaystyle{\sin{{\left(\frac{\pi}{{3}}+\frac{\pi}{{2}}\right)}}}={\sin{{\left(\frac{\pi}{{3}}\right)}}}{\cos{{\left(\frac{\pi}{{2}}\right)}}}+$
sin(pi/2)cos(pi/3)

Since $\displaystyle{\sin{{\left(\frac{\pi}{{2}}\right)}}}={1}$ and $\displaystyle{\cos{{\left(\frac{\pi}{{2}}\right)}}}={0}$ ...

Notes

Saturday, 5 July 2014

Problem in solving an indeterminate limit [0/0] $\displaystyle\lim_{{{x}\to{0}}}\frac{{{{\sin}}^{{2}}{x}}}{{{1}-{2}{\sin{{\left(\frac{{{5}\pi}}{{6}}-{x}\right)}}}{\cos{{x}}}}}$ Because I find it easier to solve it if I switch...

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In 1984, is Julia a spy? Please provide specific examples from the book. My teacher says that he knows of 17 pieces of evidence which proves that Julia...

Saturday, 5 July 2014

Problem in solving an indeterminate limit [0/0] Because I find it easier to solve it if I switch...

No comments:

Post a Comment

In 1984, is Julia a spy? Please provide specific examples from the book. My teacher says that he knows of 17 pieces of evidence which proves that Julia...

Problem in solving an indeterminate limit [0/0] $\displaystyle\lim_{{{x}\to{0}}}\frac{{{{\sin}}^{{2}}{x}}}{{{1}-{2}{\sin{{\left(\frac{{{5}\pi}}{{6}}-{x}\right)}}}{\cos{{x}}}}}$ Because I find it easier to solve it if I switch...