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Grade: upto college level

                        

Let a = min x2 + 4x + 5, x ? R and b = lim??0 1-cos 2? ?2 then find the value of a-b a+b .

6 years ago

Answers : (4)

Sher Mohammad
IIT Delhi
askIITians Faculty
174 Points
							
a=1, b=2
1-2/1+2=-1/3


Sher Mohammd
B.Tech, IIT Delhi
6 years ago
Ajay Verma
askIITians Faculty
33 Points
							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
6 years ago
Sher Mohammad
IIT Delhi
askIITians Faculty
174 Points
							

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


Sher Mohammd
B.Tech, IIT Delhi
6 years ago
Ajay Verma
askIITians Faculty
33 Points
							
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
6 years ago
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