160 - Questions Answers
If x+y = 1 ,then ∑ r nCrxryn-requals nx....How??
∑ r nCrxryn-r
= ∑ r nCrxr(1-x)n-r
= ∑ r n!/r!(n-r)! xr(1-x)n-r
= n (n-1)!/(r-1)!(n-r)! xr(1-x)n-r
= n (n-1)C(r-1) xr(1-x)n-r
= n (n-1)Cr xr+1(1-x)n-r-1 let r = r+1
= nx (n-1)Cr xr(1-x)n-r-1
now solve
How to inegrate ( In t) dt /(t-1)
let lnt = x so dt/t = dx so dt = tdx = exdx
now ∫(ln t)dt/(t-1) = ∫xexdx/(ex-1) = ∫x(ex-1+1)dx/(ex-1)
now solve
ƒ(x)=|x-2| and g=ƒoƒ so g'(x)=.......? ; 2<x<4
for 2<x<4, f(x) = x-2
so g(x) = f(x-2) = x-2-2 = x-4
so g'(x) = 1
ƒ(x)=3|2+x| so ƒ'(-3)=? ,if its -3 , how?
ƒ(x)=3|2+x|
for x>-2, f(x) = 3(2+x) so f'(x) = 3
for x<-2, f(x) = -3(2+x) so f'(x) = -3
∫√tanx
let √tanx = t
so sec2xdx/2√tanx = dt
so (1+t4)dx/2t = dt
so dx = 2tdt/(1+t4)
now solve
What is the value of 0⁄0? if its otherthan 1, then how this can be true: lim (ex-1)/x = 1
x −−>0
exact 0 and lim tends to 0 are different
what is the angular difference between the +j and -j ?
OR
+4j and -4j ?
180 degree
sin‾¹(sin2) + sin‾¹(sin4) + sin‾¹(sin6) = ?
sin‾¹(sin2) + sin‾¹(sin4) + sin‾¹(sin6)
= (π-2) + (π-4) + (6-2π)
= 0
if ƒ:R−{0} -> R, 2ƒ(x) − 3ƒ(1⁄x) = x² then ƒ(3)= ?
2ƒ(x) − 3ƒ(1⁄x) = x² (1)
so 2ƒ(1/x) − 3ƒ(x) = 1/x² (2)
multiply (1) to 2 and (2) to 3, then add the two equations, you will get f(x) then calculate f(3)
Sir/Madam,
Suddenly a question struck on my mind: 0×∞= 1 or 0?? as 1⁄0=∞.
it will be 0, assume it by considering that ∞ is a big number
for ex. 0*(1111111111111111111111111) = 0