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OpenStudy (anonymous):

need to attachment

OpenStudy (anonymous):

OpenStudy (anonymous):

what you wanna do here is multiply by the conjugate

OpenStudy (anonymous):

ok idea is this. if the limit is going to exist, since the denominator is going to 0 the numerator must go to 0 as well

OpenStudy (anonymous):

otherwise, no limit

OpenStudy (anonymous):

so replace x by 0 and solve \[\sqrt{b}-4=0\] \[b=16\]

OpenStudy (anonymous):

but how did you get the 16?

OpenStudy (anonymous):

now as lagrange said, if you want to find the limit of \[\lim_{x\rightarrow 0}\frac{\sqrt{7x+16}-4}{x}\] you have to multiply by the conjugate

OpenStudy (anonymous):

oh because i want \[\sqrt{b}-4=0\] \[\sqrt{b}=4\] \[b=16\]

OpenStudy (anonymous):

oh ok you square both sides

OpenStudy (anonymous):

well i guess. i actually just though "what number has square root 4?"

OpenStudy (anonymous):

well that work to

OpenStudy (anonymous):

you mean the conjugate which is the numerator and changing the plus to minus?

OpenStudy (anonymous):

can someone please show me step by step how to multiply by the conjugate?

OpenStudy (anonymous):

wow, you are late

OpenStudy (anonymous):

yeah well my internet connection was messed up, lol

OpenStudy (anonymous):

multiply top and bottom by \[\sqrt{7x+16}+4\] numerator will be \[7x+16-16=7x\] denominator will be \[x(\sqrt{7x+16}+4)\]

OpenStudy (anonymous):

fraction will reduce to \[\frac{7}{\sqrt{x+16}+4}\]

OpenStudy (anonymous):

now let x go to 0, get \[\frac{7}{\sqrt{16}+4}=\frac{7}{8}\]

OpenStudy (anonymous):

so is this when you would plug in the zero?

OpenStudy (anonymous):

so is this the limit?

OpenStudy (anonymous):

yes you plug in 0 when it is no longer in the denominator

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