IIT JEE , AIEEE Forum - Mathematics , Differential Calculus

jaysunantony

Evaluate :
_{[x ]}

_{[ 1]} [ 1 / |1-x| ]

Pls...............dont simply go fr the ans...........I need the expl...........

Anyway..............it do exists..........as per my Book..........

Thanks.

neeraj_agarwal_1990

RHL
for rhl, |1-x|=x-1
thus limit is 1/(approaching 0+)
=infinity

LHL
for lhl, |1-x|=1-x
limit is 1/(approaching 0 +)
=infinity

U can also observe from its graph that x=1 is a vertical asymptote and the function is always +ve...so approaching to 1 from either side will give the limiting value of y as infinity.

him26.89

look,

lx-1l is

x-1 for x>1 &

1-x for x<1

:. x->1+

i.e. 1+h

limit is equal to 1/h

so it is infinity.

for x->1-

i.e. 1-h

which is 1/h again

so ans is infinity.

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