pls solve these qns.

1)Let e be the eccentricity of a hyperbola x²/a²-y²/b²=1.  and f(e) be the eccentricity of a conjugate hyperbola then the value of the integral is


2)

3)The equation whose roots are reduced by 3 from the roots of the equation x³-3x²-4x+12=0 is denoted as f(x) .then f'(x)=_______________

ne more replis/

1/ e2 +1 /e12 =1

e1=e/rt{e2-1}

i.e f{e}=

f{f{e}} = e

f{f{f{e}}}=      

similarly f{f{....f{e}...199 times = 

now 

evaluate get the answer in  terms of e and put value of e= 

qstn 2.  sigm{x}=1 when x>0

sigm{x}=0 when x=0

sigm{x}=-1 when x<0

divide the intergral in parts and evaluate the ans..

for the third one:

put x-3 instead of x in the eqn and evalute to get f{x}

get f¹{x} to get the ans.