| Message |
|
|
Logarithm is defined for complex nos. also.
if z=x+iy
log(z)= log |z| + i tan-1(y/x)
|
|
|
|
I directly differentiated it and got the range as (3 - 2  11) /7 to 1/2
Pls let me know if it is right.
|
|
|
|
sin (  /x) >0 if  /x  ( 2n , (2n+1) )
1/x (2n,2n+1)
x ( 1/(2n+1) , 1/2n)
putting n=1,2,-1 v get the answer
so (D) is the right answer
|
|
|
|
x= (ey - e-y)/( ey+ e-y)
=> 1/x = ( ey+ e-y)/(ey - e-y)
=> (1+x) / (1-x) = (ey)/( e-y ) = e2y
=> log(1+x) / (1-x) = 2y
|
|
|
|
You can also do it like this:
let the 20 people be ABCDEFGH...
let the pairs be chosen as |AB | CD | EF | GH...
so there are 20! ways of arranging ABCDE....
In this the same arrangement repeats 10! times .
( because | AB | CD |.. and CD | AB | .. are the same.,etc.)
AB and BA are the same pair. so each of these will be repeated a total of 2^10 times.
So finally the answer is 20! / 10! * 2^10. Which is same as 19*17*15*.....5*3
|
|
|
|
20C2*18C2*16C2...........*2C2 is wrong.
Take this case : suppose the 20 people are ABCDE.... and you choose the first combination as AB CD EF..... and the second as CD AB EF ....
both these cases are the same.
I think the answer given by thevyzz is right .
|
|
|
|
I 'm getting range as (3 - 2  11) /7 to 1/2
|
|
|
|
I dont know what 's the use of substituting u,v,w.
but u can do it like this
let xlogy=a
=> logy logx= log a ( taking log on both sides and using the formula log x^n=nlogx)
=> logx logy=log a
=> ylogx =a
therefore x logy= ylog x
now substitute x logy-logz as x logy / xlogz ...
=x logy / z logx
similarly doing like this to other terms, all will get cut and u get 1.
|
|
|
|
1) f(x)=5/4 for all values of x.
therefore gof(x)=1
2) sec-1 is defined if | logx |  1
=> x  1/e or x  e
but log x is defined for +ive values
=> x (0,1/e] U [e,inf)
|
|
|
|
If there are other solutions , they should also solve the equations.
The fact that we get 2 linear equations in 2 variables itself proves that there are no other solutions.
|
|
|
|
use the log formulas log(ab)=log(a)+log(b)
log(a/b)=log(a)-log(b)
log(a^n)=nlog(a)
on simplifying (1+64-36-28)log2+(-16-12+28)log3+(-16+24-7)log5
=log2+log5
=log(10)
(Answer corrected)
|
|
|
|
there is a small mistake in your answer.
[n(n+1)/12] [n(n+1)+2n+1+1]
={n(n+1)/12} (n²+3n+2)
=n(n+1)(n+1)(n+2)/12
|
|
|
|
Just substitute the value of x in the equation.
As a and b are integers , the rational and irrational parts can be equated separately.
so a=-12 , b= 6
|
|
|
|
you can take the required point P as (x,x) [ y=x because P lies on the line y=x]
find PA and PB using distance formula
find minimum of PA-PB using differentiation.
this solution is correct but the differentiating part is too big.
|
|
|
|
|
