Q the value of lim x tends to k- x-[x] is A lim h tends to 0 k-h-[k-h] - Maths - Limits and Derivatives

Question

Q the value of lim x tends to k- x-[x] is
A lim h tends to 0 k-h-[k-h]
= what to do next sir
in book they are doing like this
= lim htends to 0 k-h-(k-1) = 1
how are they puting 1 over ther ? plz explain

Sanjay Kumar Manjhi · Accepted Answer

Dear Student,limx→k-x-[x]Here limit is k-, which is Left Hand Limit
Now,Let h→0⇒x→k-hNow,=limh→0-(k-h)-[k-h]As we mentioned earlier it is a Left Hand Limit
 So even if k is a integer if we take left hand limit
Greater Integer Function will reduce it to -1
So,=limh→0-(k-h)-[k-h]=limh→0-(k-h)-(k-1)=k-(k-1)=1Regards

Q. the value of lim x tends to k- x-[x] is A. lim h tends to 0 k-h-[k-h] = what to do next sir in book they are doing like this = lim htends to 0 k-h-(k-1) = 1 how are they puting 1 over ther ? plz explain.

Q. the value of lim x tends to k^- x-[x] is
A. lim h tends to 0 k-h-[k-h]
= what to do next sir
in book they are doing like this
= lim htends to 0 k-h-(k-1) = 1
how are they puting 1 over ther ? plz explain.