Question

lim ((1/c+h)-(1/c))/h
h → 0

Answer 1

\[\lim_{h \rightarrow 1} \frac{ ((\frac{ 1 }{ c+h })-(\frac{ 1 }{ c })) }{ h }\] To make the equation more clear.

Answer 2

sorry, as h-->0

Answer 3

put over common denominator
c-c+h
______ = h/(c+h)h=1/(c+h) / h= 1/(c+h)h= 1/(c+0)0 = 1/0=+infinity
(c+h)h

Answer 4

\[\lim_{h \to 1} \frac{ \dfrac{ 1 }{ c+h }-\dfrac{ 1 }{ c } }{ h }\\
\lim_{h \to 1} \frac{ \dfrac{ c }{ c(c+h) }-\dfrac{ c+h }{ c(c+h) } }{ h }\\
\lim_{h \to 1} \frac{ \dfrac{ c -c-h}{ c(c+h) }}{ h }\\
-\lim_{h \to 1} \frac{ \dfrac{ h}{ c(c+h) }}{ h }\\
-\lim_{h \to 1} \dfrac{1}{ c(c+h) }=\cdots
\]