Use algebra to evaluate the limit as h approaches 0.

Question

Use algebra to evaluate the limit. Use lower case letters.
lim      ((1/(c+h))- (1/c))/h
h→0

I have tried to work out the algebra so many times but I get different answers each time and the c's don't eliminate like they did in my professors similar example. Please help me, I am so confused.

Answer 1

You want the h's to cancel each other out.  Here is the process.

 

 

In the numerator part, the LCD is c(c + h).

 

 

 

lim               c - (c + h)        *        1

               _____________           _____

h->0             c(c + h)                    h

 

 

 

lim                  -h

h->0      ____________

                  hc(c + h)

 

 

 

lim             - 1

h->0    _________

               c(c + h)

 

 

Plug in h=0.

 

lim          - 1

h->0    _______

               c²

 

 

limit is     -1/c².

 

 

If  f(x)=1/c, then the limit is the derivative of f(x).

 

f(x) = c^-1

 

f'(x) = -c^-2

 

f(x) = -1/c²