# Let a = min x2 + 4x + 5, x ? R and b = lim??01-cos 2??2then find the value ofa-ba+b .

10 years ago
`$\text{MinValue}\left[x^2+4 x+5,x\right]=1$$\lim_{x\to 0} \, \frac{1-\cos (2 x)}{x^2}=2$a=1, b=21-2/1+2=-1/3Sher MohammdB.Tech, IIT Delhi`
Ajay Verma
10 years ago
ans:

a= min (x^2+ 4x +5)
( using dy/dx= 0 at critical points)
y= x^2+ 4x +5 ; dy/dx = 2x+4 = 0 so x = -2
d2y/dx2= 2(-2) + 4 = 1 so minimum..

so a = 1

b = lim y --> 0 = (1- cos 2y)/ y2: 0/0 form so use DL hospi low..
b= lim y-->0 = 2 sin2y / 2y ; lim y-->0 sin 2x/ 2x = 1
soo b= 2

a-b/ a+b = 1-2 / 1+2 = -1/3

Thanks and Regards,
Ajay verma,
10 years ago
`$\text{MinValue}\left[x^2+4 x+5,x\right]=1$$\lim_{x\to 0} \, \frac{1-\cos (2 x)}{x^2}=2$1-2/1+2=-1/3Sher MohammdB.Tech, IIT Delhi`
Ajay Verma
10 years ago

solution:

a= min (x^2+ 4x +5)
( using dy/dx= 0 at critical points)
y= x^2+ 4x +5 ; dy/dx = 2x+4 = 0 so x = -2
d2y/dx2= 2(-2) + 4 = 1 so minimum..

so a = 1

b = lim y --> 0 = (1- cos 2y)/ y2: 0/0 form so use DL hospi low..
b= lim y-->0 = 2 sin2y / 2y ; lim y-->0 sin 2x/ 2x = 1
soo b= 2

a-b/ a+b = 1-2 / 1+2 = -1/3

Thanks and Regards,
Ajay verma,