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How do I determine #lim_(x->0.5^-)(2x-1)/|2x^3-x^2|#, if it exists?

Answer 1

Christopher Allers

#lim_(x->0.5^-)(2)/(-6x^2+2x)=2/[1-1.5]=2/-0.5=-4#

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#lim_(x->0.5^-)(2x-1)/|2x^3-x^2|#

since x purchase from left

#lim_(x->0.5^-)(2x-1)/-(2x^3-x^2)=lim_(x->0.5^-)(2x-1)/(-2x^3+x^2)#

#=[2(0.5)-1]/[(0.5)^2-2(0.5)^3]=[1-1]/[(0.25)-2(0.125)]#

#0/[0.25-0.25]=0/0#

since the direct compnsation product equal #0/0# we should lohpital rule

#lim_(xrarra)[f'(x)]/[g'(x)]#

#lim_(x->0.5^-)(2)/(-6x^2+2x)=2/[1-1.5]=2/-0.5=-4#

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Answer 2

Christopher Allers

To determine the limit as x approaches 0.5 from the left of the expression (2x-1)/|2x^3-x^2|, we can evaluate the expression by substituting the value of x into the expression. If the resulting expression is defined and finite, then the limit exists.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

How do I determine #lim_(x-&gt;0.5^-)(2x-1)/|2x^3-x^2|#, if it exists?

How do I determine #lim_(x->0.5^-)(2x-1)/|2x^3-x^2|#, if it exists?