Lim x#rarr# #oo# 2#sqrt#x +(#x^-1#)/3x-7 help me to find the limit?

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Answer 1 · 2017-10-30T22:35:14

#0#

Writing as:

#(2x^(1/2)+x^-1)/(3x-7)#

Plugging in #oo# would give us the indeterminate form #oo/oo#

Using L'Hosipal's Rule:

To use this rule, we differentiate numerator and denominator.

Differentiating numerator:

#dy/dx (2x^(1/2)+x^-1)= x^(-1/2) -x^-2=1/sqrt(x)-1/x^2#

Differentiating denominator:

#dy/dx (3x-7)=3#

#:.#

#lim_(x->oo)(1/sqrt(x)-1/x^2)/(3)= (0-0)/3=0#