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Calculate this limit using Wolfram Language?

Posted 5 months ago
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lim(x->0+) (x^(a) log(x))/(log(1 + x^2) (sin(x^2) - sin^2(x))) a>0

If $a > 0$ :

 Limit[(x^a Log[x])/(Log[1 + x^2] (-Sin[x]^2 + Sin[x^2])), x -> 0, Direction -> "FromAbove", Assumptions -> a > 0]

 (*  ConditionalExpression[0, a > 6] *)

and $0<a\leq 6$ then:

 Limit[(x^a Log[x])/(Log[1 + x^2] (-Sin[x]^2 + Sin[x^2])), x -> 0, Direction -> "FromAbove", Assumptions ->0 < a <= 6]

 (*  ConditionalExpression[-\[Infinity], a < 0]  *)
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