Let k>0 and λ=limx→0 k1−4k2−x2x2k2−x2 be finite. Then the value of λk, is

It is given that       λ=limx→0 k1−4k2−x2x2k2−x2 exists⇒ limx→0 k1−4k2−x2=0⇒1−4k=0⇒k=14∴ λ=limx→0 1−1−16x2x21−16x2⇒ λ=limx→0 1−1−16x2x21+1−16x21−16x2⇒ λ=16limx→0 11+1−16x21−16x2=8Hence, λ=8 and k=14