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question mark

Let a = min x2 + 4x + 5, x ? R and b = lim??0\n1-cos 2?\n?2\nthen find the value of\na-b\na+b .

REDDEIAH , 10 Years ago
Grade upto college level
anser 4 Answers
Sher Mohammad

Last Activity: 10 Years ago 

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


Sher Mohammd
B.Tech, IIT Delhi

Ajay Verma

Last Activity: 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,
askIITians faculty,
IIT HYDERABAD

Sher Mohammad

Last Activity: 10 Years ago 


1-2/1+2=-1/3


Sher Mohammd
B.Tech, IIT Delhi

Ajay Verma

Last Activity: 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,
askIITians faculty,
IIT HYDERABAD

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