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Open the series of cosx e^xand e^-xby power series method .....

Now use two concepts .. these are to be used in general while solving such questions

First the limit has to exist so the constant and coefficeint with x have to be zero since we have xsinx in the denominator ...

Second the coefficent of x² term should give the limit .....

I hope this helps .. reply back to this post if things are not clear ..

cheers !!!

Let the two parts be x and y ..

So we have two equations

x + y = 30000

and 0.09x + 0.11y = 3060

Now write these equations as a matrix and we are done !!!

cheers

Well both Delhi and Kota are good places to do JEE preparation. Both places have many good coaching institutes. However what matters is the fact that u do hard work .. okay ..

Well the study material of Brilliant is better however the classroom coaching of Vidyamandir is better ..

Again such things are perceptions that a individual has .. all depends as to what u like ...
Also I will suggest that once u join the coaching institute then study material that those suggest you to do so that there is a better coordination between you and your classes ...

cheers

Well yes this is correct !!

If u want to find the range then this is also fine ... all depends on what the question demands !!

This answer seems to be perfecto !!! Gr8 work done !!

The books which represent sgn(x) as mod(x)/x have defined it wrong. The actual definition is as follows :

sgn(x) = mod(x)/x when x

0

= 0 when x = 0

Now the thing should be hopefully clear ......

Cheers

It is okay dear ... the syllabus for iit do not chnage much .... or let me put it this way that even if it changes the books remain the same ... a new edition of M.L. khanna wud just have a new cover and nothing more than that .. so u can use the book u have purchased and there is no need to worry about ...

cheers

Gr8 answer ... rahul gr8 work done ..

cheers

hiiii

All the above suggested solutions are valid ..

See the key point is that u try to understand the concepts .. use some book say Arihant's book and start going through the theory of one chapter, once u know the theory then start solving problems ... going from easy to hard level .

While u solve problems focus on the concepts rather than the craming of way to solve the problems ... gradually u will start understanding the topics .. n u will not face any problem ..

Keep confidence in urself ... cheerooo

Put cos 2x = 1 / t

So, dx = dt / ( 2t². sin 2x)

so,

cos2x/sinx =

dt / ( 2t². 2sin²x) *

t * cosx

=

dt /

2 * t(t-1)

t+1

Now put t + 1 = p²

So,

cos2x/sinx =

2* dp / (p² - 1)*( p² - 2 )

=

2* dp / ( p² - 2 ) -

2* dp / ( p² - 1 )

Now these integrals can be easily intergated and thus we are done by resubstituting the values of p.

Cheers !!!!!!!!!!!!

y = log₁₀ x + log _x 10 + log _xx + log₁₀ 10
= log_ex / log_e10 + log_e10/log_ex + 1 + 1

dy/dx = 1 / (x * log_e10) - log_e10/((log_ex)²* x) + 0
= 1 / (x * log_e10) - log_e10/((log_ex)²* x)

cheers !!!!!

Correct answer .... well done !!!

The answer is C since we do not know that the force is applied in which direction and what is the direction of the displacement.

Note that the work done if F.d !!!!

cheers

Absolutely correct answer !!!! good work !!!!

Thank god u got it ........