Let L = lim    [a - sqrt(a- x) - (x/4)] /  x, a > 0.
            x--0

If L is finite, then

a). a = 2; L = 1/64
b). a = 1; L = 1/64
c). a = 3; L = 1/32
d). a = 1; L = 1/32

Dear Student,
Please find below the solution to the asked query:

L=limx0 a-a2-x2-x24x4=limx0 a-x24 -a2-x2x4=limx0 a-x24 -a2-x2x4a-x24 +a2-x2a-x24 +a2-x2=limx0 a-x24 2-a2-x2x41a-x24 +a2-x2=limx0 a2+x416-2ax24 -a2+x2x41a-x24 +a2-x2=limx0 x416-ax22 +x2x41a-0 +a2-0=limx0 x416+x21-a2x41a+aFor limit to be finite, x4 in denominator must get cancelled, hence coefficientof x2 in numerator must be 0.1-a2=0a=2HenceL=limx0 x416+0x412+2=limx0 11614=116×4=164Hence a=2 and L=164

Hope this information will clear your doubts about this topic.

If you have any doubts just ask here on the ask and answer forum and our experts will try to help you out as soon as possible.
Regards

  • 8
What are you looking for?