is this solvable2

Discuss continuity of e[log{l{x2}l2}]
and draw its graph

where all brackets have their usual meaning...


dont hesitate to tell me if it is not solvable at our level

1 Answers

1
Samarth Kashyap ·

consider x to lie in [√n,√(n+1))....nεN
x2 ε [n , n+1)
[x2]=n....therefore,{x2}=x2-n

e[log{l{x2}l2}]

e[log{l(x2-n)l2}].....for x2 ε [n,n+1)
|x2-n|≤1.....therefore, {|x2-n|2}=(x2-n)2

hence, f(x)=e[2ln(x2-n)]

considering the limit at the points where x=√n....it can be easily seen tht the function is discontinuous for x=√n...nεN

the other points of discontinuity can be got by considering the continuity of [2ln(x2-n)]

considering, 2ln(x2-n) ε {(-1,0),(-2,-1),(-3,-2).......},the points of discontinuity can be found out.

the points of discontinuity are,
x=√n....for all nεN
x=\sqrt{e^{\frac{-k}{2}}+n} for all kεN and for any particular nεN

pls correct me if i'm wrong...also help me with the graph

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