Use a CAS to plot the function near the point x0 being approached. From your plot guess the value of the limit.
-Write the formal notation for the principle "the limit of a quotient is the quotient of the limits" and include a statement of any restrictions on the principle.
A)

\lim _ { x \rightarrow a } \frac { g ( x ) } { f ( x ) } = \frac { g ( a ) } { f ( a ) }

.
B) If

\lim _ { x \rightarrow a } g ( x ) = M

and

\lim _ { x \rightarrow a } f ( x ) = L

, then

\lim _ { x \rightarrow a } \frac { g ( x ) } { f ( x ) } = \frac { \lim _ { x \rightarrow a } g ( x ) } { \lim _ { x \rightarrow a } f ( x ) } = \frac { M } { L }

, provided that

L \neq 0

.
C) If

\lim _ { x \rightarrow a } g ( x ) = M

and

\lim _ { x \rightarrow a } f ( x ) = L

, then

\lim _ { x \rightarrow a } \frac { g ( x ) } { f ( x ) } = \frac { \lim _ { x \rightarrow a } g ( x ) } { \lim _ { x \rightarrow a } f ( x ) } = \frac { M } { L }

, provided that

f ( a ) \neq 0

.
D)

\lim _ { x \rightarrow a } \frac { g ( x ) } { f ( x ) } = \frac { g ( a ) } { f ( a ) }

, provided that

f ( a ) \neq 0

Find the Slope of the Curve at the Given Point y=x3−8x,P(1,−7)y = x ^ { 3 } - 8 x , P ( 1 , - 7 )y=x3−8x,P(1,−7)

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Find the Slope of the Curve at the Given Point $y = x ^ { 3 } - 8 x , P ( 1 , - 7 )$

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