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Please be specific. And to my knowledge alkyl halides are involved in p-sp3 in normal alkyl and p-sp2 in vinyl and aryl halides.

For the third, Don't say limit doesn't exist. It exists and it is infinity.

One more easy one:

1.Prove the parallelogram law of vectors i.e. |a+b|=?

Yes right.

First give your solutions.

I started a new thread for this

1.Prove angle in a semicircle is 90.

2.Prove that in a rhombus diagonals bisect each other at right angles.

Yes that's what I meant

Appyling LHL and RHL we get it is continuous for all x in R

I think the function second part is greater than or equal to 2

1.Prove angle in a semicircle is 90.

2.Prove that in a rhombus diagonals bisect each other at right angles.

First divide and get it as,

=1+(7x^2 +19)/[(x²+3)(x²-5)]

Then do partial fractions and hence get the answer

Multiply and divide by 2.

Then write 2=1-x^2 + 1+x^2

separate it into two integrals and

Divide by x^2 in both of them,

For the first substitute x+1/x =y

For the second sub. x-1/x =z

then solve

$\int \frac {\cos ^{3}{x} + \cos ^{5}{x}}{\sin ^{2}{x} + \sin ^{4}{x}}\,dx$

= $\int \frac {\cos ^{3}{x}\cdot(1 + \cos ^{2}{x})}{\sin ^{2}{x} + \sin ^{4}{x}}\,dx$

Put $\sin{x} = t$ obviously, $dt = \cos{x}\cdot dx$

= $\int \frac {(1 - t^{2})\cdot (2 - t^{2})}{t^{2}\cdot (1 + t^{2})}\,dt$

= $\int \frac {t^{4} - 3\cdot t^{2} + 2}{t^{2}\cdot (1 + t^{2})}\,dt$

= $\int 1 + (\frac {2 - 4\cdot t^{2}}{t^{2}\cdot (1 + t^{2})})\,dt$

Doing partial fractions we get,

= $\int 1 + \frac {2}{t^{2}} - \frac {6}{1 + t^{2}}\,dt$

= $t - \frac {2}{t} - 6\cdot \tan^{ - 1} {t} + C$

= $\sin{x} - 2\cdot cosec x - 6\cdot \tan^{ - 1} {\sin{x}} + C$