Mathematics, 30.07.2019 13:40 lalala1212

$\lim_{x \to \-6} \frac{ \sqrt{x^{2}+12x+36 } }{x+6}$ can someone verify that the limit does not exist? i got -1 from the left and 1 from the right. the limit is to negative 6. i used the math text tool but the negative sign isn't showing up on my screen.

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Just as a tip: the source says you typed it in as\lim_{x \to \-6}, which results in $\lim_{x \to \-6}$ the \- is a command. backslashes are used to denote commands in latex, which is what this site's math tool is based off of. if you put a backslash in front of the hyphen, the tex compiler will not recognize it as a negative. so enter it simply as \lim_{x \to -6}, which results in $\lim_{x \to -6}$ .if you want it under, use the command \displaystyle in front. the limit in front right now is considered "textstyle," or "inline math."\lim_{x \to -6} results in $\lim_{x \to -6}$ \displaystyle\lim_{x \to -6} results in $\displaystyle\lim_{x \to -6}$ using \displaystyle also makes fractions look less compact, making them slightly easier to read. (however, this does make it look too big for use in paragraphs, so i usually use these on separate "paragraphs.")\frac{\sqrt{x^2 + 12x+36}}{x+6} results in $\frac{\sqrt{x^2 + 12x+36}}{x+6}$ \displaystyle\frac{\sqrt{x^2 + 12x+36}}{x+6} results in $\displaystyle\frac{\sqrt{x^2 + 12x+36}}{x+6}$ or use \dfrac{}{} for display fractions. this does not need \displaystyle: \dfrac{\sqrt{x^2 + 12x+36}}{x+6} results in $\dfrac{\sqrt{x^2 + 12x+36}}{x+6}$ yes, the limit does not exist. graphical evidence is shown below. algebraic evidence: $\displaystyle \lim_{x \to -6} \dfrac{\sqrt{x^2 + 12x + 36}}{x+6} = \displaystyle \lim_{x \to -6} \dfrac{\sqrt{(x+6)^2}}{x+6} = \displaystyle \lim_{x \to -6} \dfrac{|x+6|}{x+6}$ for left side, we have (typed as \displaystyle\lim_{x \to -6^-}) $\displaystyle \lim_{x \to -6^-} \dfrac{|x+6|}{x+6} = \displaystyle \lim_{x \to -6^-} \dfrac{-(x+6)}{x+6} = \displaystyle \lim_{x \to -6^-} (-1) = -1$ for right side, we have (typed as \displaystyle\lim_{x \to -6^+}) $\displaystyle \lim_{x \to -6^+} \dfrac{|x+6|}{x+6} = \displaystyle \lim_{x \to -6^-} \dfrac{+(x+6)}{x+6} = \displaystyle \lim_{x \to -6^-} (1) = 1$ so yes, does not exist

Answer from: Quest

total amount to be paid = $19.5

step-by-step explanation:

given ,

original price = $25.99

discount = 25%

discount amount = 25% of original price

discount amount = 25/100 * 25.99

discount amount = $6.49

hence , the total amount to be paid = original price - discount amount

= $25.99 - $6.49

=$19.5

total amount to be paid = $19.5

Answer from: Quest

dude thats to long figure it

step-by-step explanation:

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[tex] \lim_{x \to \-6} \frac{ \sqrt{x^{2}+12x+36 } }{x+6} [/tex] can someone verify that the limit d...

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