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Let a = min( x^2 + 4x + 5, x belongs to R) and b= lim??0 1-cos 2?/?^2 then find the value of a-b/a+b .(here ? means theta)

Let a = min( x^2 + 4x + 5, x belongs to R) and b= lim??0 1-cos 2?/?^2
then find the value of
a-b/a+b .(here ? means theta)

Grade:Upto college level

1 Answers

Ajay Verma
askIITians Faculty 33 Points
7 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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