Question

Please love limit class 12th​

Answer 1

Important formulae,used to solve

cos(A)-cos(B)=-2sin(A+B)/2 cos(A-B)/2

So,here in this question

cos(x+1)^1/2 -cosx^1/2=-2sin{(x+1)^1/2+x^1/2}/2 ×sin{(x+1)^1/2-x^1/2}/2

on,Rationalizing sin{(x+1)^1/2-x^1/2)

=-2{sin(x+1)^1/2 +x^1/2}1/2 ×sin{(x+1)^1/2-x^1/2}{(x+1)^1/2+x^1/2)/2({x+1)^1/2+x^1/2)}

=-2{sin(x+1)^1/2 +x^1/2}/2 ×sin(x+1-x)/{(x+1)^1/2 +x^1/2}

now put x=infinity

=-2sin(infinite)×sin(1/infinite)

=-2sin(infinite)×sin0....(1/infinite=0)

=-2sin(infinite)×0

since we know,in the value of sinx always is between -1 to 1

so,

sin(infinite)=finite no. between -1 to

=-2×finite number×0

=0

so,value of limit will be 0

{hope it helps}

Answer 2

sorry for my bad handwriting...

...btw you asked me to "love" limit

xD