Question #1ec73

2 Answers
Steve M
Mar 16, 2017

# lim_(x to oo) (x^2/2-x)(0^2/2-0) = 0#

Explanation:

We want to find:

# lim_(x to oo) (x^2/2-x)(0^2/2-0) #

If we examine the limit function, we have;

# (x^2/2-x)(0^2/2-0) = (x^2/2-x)(0) = 0#

Hence,

# lim_(x to oo) (x^2/2-x)(0^2/2-0) = 0#

Alan P.
Mar 16, 2017

#lim_(xrarroo) ((x^2)/2-x)((0^2)/2-0)=color(green)(0)#

Explanation:

#((0^2)/2-0)=0#

Any defined value multiplied by #0# equals #0#.

The possible conceptual problem here is in trying to take the given expression as:
#color(white)("XXX")oo xx 0 = ???# (undefined)
but
#color(white)("XXX")lim_(xrarr0)# does not mean that #x# is ever actually #=0#
and for any value #barx!=0#
#color(white)("XXX")((barx^2)/2-barx)# is defined, say as some (defined) value #v#
#color(white)("XXX")#and
#color(white)("XXX")v xx 0 = 0#

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