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Substitution Method to Remove Indeterminate Form

Solve: lim u...

Question

Solve:
${lim}_{u \to 1} \frac{\sqrt{u^{2} + 8}}{\sqrt{u^{2} + 3}} - \frac{\sqrt{10 - u^{2}}}{\sqrt{5 - u^{2}}}$

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Solution

$l i m_{u \to 1} \frac{\sqrt{u^{2} + 8}}{\sqrt{u^{2} + 3}} - \frac{\sqrt{10 - u^{2}}}{\sqrt{5 - u^{2}}}$

$= \sqrt{\frac{9}{4}} - \sqrt{\frac{9}{4}}$

$= 0$

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Similar questions

y = tan (\frac{1}{2} {cos}^{- 1} \frac{1 - u^{2}}{1 + u^{2}} + \frac{1}{2} {sin}^{- 1} \frac{2 u}{1 + u^{2}})

x = \frac{2 u}{1 - u^{2}}

\frac{d y}{d x}

y = t a n (\frac{1}{2} c o s^{- 1} \frac{1 - u^{2}}{1 + u^{2}} + \frac{1}{2} s i n^{- 1} \frac{2 u}{1 + u^{2}})

x = \frac{2 u}{1 - u^{2}}

\frac{d y}{d x}

\frac{1}{2} \int \frac{u^{2}}{1 + u} d u

U_{1}, U_{2}, U_{3}

represents the potential energy of mass

m

moving from A to B along three different paths

1

2

3

(as shown in the figure) in the gravitational field, then

U_{1}, U_{2}, U_{3}

represent the potential energy differences for moving a particle from

A

B

along three different paths

1, 2 & 3

(as shown in the figure) in the gravitational field of point mass

m

, find the correct relation between

U_{1}, U_{2} & U_{3}

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Substitution Method to Remove Indeterminate Form

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