Find the Limit...6

[nycmathguy]

Calculus
Section 1.6

 

[MathLover1]

18 and 20 are correct

22. correction:

lim((sqrt(4x+1)-3)/(x-2),x->2)

rationalize numerator:
((sqrt(4x+1)-3)(sqrt(4x+1)+3))/((x-2)(sqrt(4x+1)-3))

=((4x+1)-9)/((x-2)(sqrt(4x+1)+3))

=(4x-8)/((x-2)(sqrt(4x+1)+3))

=(4(x-2))/((x-2)(sqrt(4x+1)+3)).......simplify

= 4/(sqrt(4x+1)+3)

then

lim(4/(sqrt(4x+1)+3),x->2)=4/(sqrt(4*2+1)+3)=4/(sqrt(9)+3)=4/(3+3)=4/6=2/3

 

[nycmathguy]

18 and 20 are correct

22. correction:

lim((sqrt(4x+1)-3)/(x-2),x->2)

rationalize numerator:
((sqrt(4x+1)-3)(sqrt(4x+1)+3))/((x-2)(sqrt(4x+1)-3))

=((4x+1)-9)/((x-2)(sqrt(4x+1)+3))

=(4x-8)/((x-2)(sqrt(4x+1)+3))

=(4(x-2))/((x-2)(sqrt(4x+1)+3)).......simplify

= 4/(sqrt(4x+1)+3)

then

lim(4/(sqrt(4x+1)+3),x->2)=4/(sqrt(4*2+1)+3)=4/(sqrt(9)+3)=4/(3+3)=4/6=2/3

I see my error. The denominator should include positive 3 not negative 3.