Find Limit of f(x)

[nycmathguy]

Calculus
Section 1.6

Can you do 59 as a guide for me to do 60?

 

[MathLover1]

lim((f(x)-8)/(x-1), x->1)=10, find lim(f(x)) as x->1

use quotient rule

lim((f(x)-8), x->1)/lim(x-1, x->1)=10

lim((f(x)-8), x->1)=10*lim(x-1, x->1)..........for left side use difference rule

lim((f(x), x->1)- lim(8, x->1)=10*lim(x-1, x->1)............lim(8, x->1)=8

lim((f(x), x->1)-8=10*lim(x-1, x->1)......lim(x-1, x->1)=0

lim((f(x), x->1)=10*0+8

lim((f(x), x->1)=8

 

[nycmathguy]

lim((f(x)-8)/(x-1), x->1)=10, find lim(f(x)) as x->1

use quotient rule

lim((f(x)-8), x->1)/lim(x-1, x->1)=10

lim((f(x)-8), x->1)=10*lim(x-1, x->1)..........for left side use difference rule

lim((f(x), x->1)- lim(8, x->1)=10*lim(x-1, x->1)............lim(8, x->1)=8

lim((f(x), x->1)-8=10*lim(x-1, x->1)......lim(x-1, x->1)=0

lim((f(x), x->1)=10*0+8

lim((f(x), x->1)=8

I will try 60 on my day off.

 

[nycmathguy]

lim((f(x)-8)/(x-1), x->1)=10, find lim(f(x)) as x->1

use quotient rule

lim((f(x)-8), x->1)/lim(x-1, x->1)=10

lim((f(x)-8), x->1)=10*lim(x-1, x->1)..........for left side use difference rule

lim((f(x), x->1)- lim(8, x->1)=10*lim(x-1, x->1)............lim(8, x->1)=8

lim((f(x), x->1)-8=10*lim(x-1, x->1)......lim(x-1, x->1)=0

lim((f(x), x->1)=10*0+8

lim((f(x), x->1)=8

I tried doing 60 a few times. I give up. My work is not even close to what you did on 59. I am lost. Can you please do 60?

 

[MathLover1]

if lim (f(x)/x^2)=5 as x->0, find following limits

use quotient rule

so, lim (f(x))/lim(x^2)=5 as x->0

a.

lim (f(x))/lim(x^2)=5

lim (f(x))=5 lim(x^2) .....as x->0

lim (f(x))=5 lim(0^2) =5*0=0


b.

lim (f(x)/x) as x->0

lim (f(x)/x)=lim (f(x))/lim(x) ...as x->0

substitute lim (f(x))=0...as x->0

lim (f(x))/lim(x) ...as x->0=lim 0/lim(0)=0

 

[nycmathguy]

if lim (f(x)/x^2)=5 as x->0, find following limits

use quotient rule

so, lim (f(x))/lim(x^2)=5 as x->0

a.

lim (f(x))/lim(x^2)=5

lim (f(x))=5 lim(x^2) .....as x->0

lim (f(x))=5 lim(0^2) =5*0=0


b.

lim (f(x)/x) as x->0

lim (f(x)/x)=lim (f(x))/lim(x) ...as x->0

substitute lim (f(x))=0...as x->0

lim (f(x))/lim(x) ...as x->0=lim 0/lim(0)=0

Very good. Visit the link below and tell me if my work is correct.

Limit of Greatest Integer Function...1