Evaluate [tex]$\lim _{x \rightarrow 5} \frac{\frac{1}{x}-\frac{1}{5}}{x-5}$[/tex] algebraically by simplifying if possible, then using direct substitution.
a.) [tex]$\lim _{x \rightarrow 5} \frac{\frac{1}{x}-\frac{1}{5}}{x-5}$[/tex] does not exist
b.) [tex]$\lim _{x \rightarrow 5} \frac{\frac{1}{x}-\frac{1}{5}}{x-5}=0$[/tex]
c.) [tex]$\lim _{x \rightarrow 5} \frac{\frac{1}{x}-\frac{1}{5}}{x-5}=-\frac{1}{25}$[/tex]
d.) [tex]$\lim _{x \rightarrow 5} \frac{\frac{1}{x}-\frac{1}{5}}{x-5}=\frac{1}{25}$[/tex]
Answer (3)
first subtract 100v² from both sides to get:
C²L²=100c²-100v²
Then divide both sides by C²:
L²=(100c²-100v²)/C²
Then take the square root of both sides:
L=+ or - the square root of (100c²-100v²)/C²
L = ±√( (100c² - 100v²) / C² ) ;
To solve for L in the equation C 2 L 2 + 100 v 2 = 100 c 2 , isolate L and simplify to find L = C 10 c 2 − v 2 . This expression gives the positive length in terms of c , v , and C .
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