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avatar+55 

I have 2 problems I need help with:

  1. \(\lim_{h\rightarrow 0}\frac{(1+h)^2-1^2}{h}\)
  2. \(\lim_{x\rightarrow 4}\frac{\sqrt(x)-2}{x-4}\)

I don't understand the answer to number 1 and I don't understand what method to use with number 2. Some help would be very much appreciated. 

 Apr 30, 2018
 #1
avatar+101870 
+2

.1.

 

lim             (1 + h)^2  - 1^2

h →0        _____________

                         h

 

 

lim      ( 1 + 2h  + h^2  -  1)

h →0  ________________

                        h

 

lim       2h  +  h^2

h →0  ________

                  h

 

 

lim           h  ( 2  + h)

h →0  ____________

                  h

 

lim         2 +  h          =         2

h →0

 

 

 

lim           √x  -  2

h → 4      ________            we can factor the denominator  as

                 x   -   4   

 

lim                  √x - 2

h → 4        ___________

               (√ x - 2) (√x + 2)

 

lim                1                           1                            1                 1

h → 4      _______     =        _______       =      _______ =     ___  

                 √x + 2                   √4 + 2                     2  + 2             4

 

 

 

cool cool cool

 Apr 30, 2018
 #2
avatar+10413 
+2

I have 2 problems I need help with:

laugh

 Apr 30, 2018
edited by Omi67  Apr 30, 2018
edited by Omi67  Apr 30, 2018

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