Solve- lim - -4 sin- -cos- - -4

It is 00 form, By l'opital L=lim_α→π4cosα +sinα1=cosπ4+sinπ4=1√(2)+1√(2)=√(2) . ...

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Particular Solution of a Differential Equation

Solve: lim ...

Question

Solve: $lim α \to π / 4 \frac{sin α - cos α}{α - π / 4}$

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Solution

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lim α \to \frac{π}{4} \frac{sin α - cos α}{α - \frac{π}{4}} =

0 < α, β < \frac{π}{4}, cos (α + β) = \frac{4}{5}, sin (α - β) = \frac{5}{13}

tan 2 α =

{sin}^{4} α + 4 {cos}^{4} β + 2 = 4 \sqrt{2}

sin α

cos β; α, β ϵ [0, π]

cos (α + β) - cos (α + β)

cos (α + β) = \frac{4}{5}

sin (α - β) = \frac{5}{13}

0 \leq α, β \leq \frac{π}{4}

tan 2 α =

cos (α + β) = 4 / 5, sin (α - β) = 5 / 13

α, β

0

\frac{π}{4}

tan 2 α

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