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Babynini
 one year ago
More limits..
Babynini
 one year ago
More limits..

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Babynini
 one year ago
Best ResponseYou've already chosen the best response.2I'm trying to rationalize but I keep going off somewhere.

Empty
 one year ago
Best ResponseYou've already chosen the best response.4Yeah that would be my first choice too, to multiply by this form of 1 and see what happens: \[\large \frac{\sqrt{x^2+9}+5}{\sqrt{x^2+9}+5}\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0\[\lim_{x \rightarrow 4}\frac{ \sqrt{x^2+9}5 }{ x+4 }\]

Babynini
 one year ago
Best ResponseYou've already chosen the best response.2@Empty the problem is i'm not quite sure how to multiply those..heh

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0hint: First define what type of form it falls under

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Just judging by the left and right hand limit type, and the form, you can apply LH rule to this.

Empty
 one year ago
Best ResponseYou've already chosen the best response.4In a lot of ways I really look at calculus as 'mastering algebra' Let's just look at the numerator or denominator one at at time, first the numerator: \[(\sqrt{x^2+9}5)(\sqrt{x^2+9}+5)\] What do we do? Well, it turns out we distribute, just like we would here even though it looks more complicated, try to fit it to this pattern if it helps you keep things straight: \[(ab)(a+b)=a*a+a*bb*ab*b = a^2b^2\] (notice the middle terms cancel out, which is super handy to save time) Give it a shot, the work you put in now will make a difference later in the semester and during tests.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0\[\left( \sqrt{x^2+9}5 \right) \times \frac{ \left( \sqrt{x^2+9}+5 \right) }{ \left( \sqrt{x^2+9}+5 \right) }=\frac{ \left( \sqrt{x^2+9} \right)^25^2}{\sqrt{x^2+9}+5}\]

Babynini
 one year ago
Best ResponseYou've already chosen the best response.2ah k @Empty let me try hahaa

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0So you want to simply this function to a form where you can input your limit value to break free from the \(\dfrac{0}{0}\) form. Take the derivative of the numerator an the denominator. \[\lim_{x\rightarrow 4} \frac{\frac{d}{dx}(\sqrt{x^2+9}5)}{\frac{d}{dx}(x+4)}\]\[\lim_{x\rightarrow 4}\frac{\frac{1}{2}(x^2+9)^{1/2} \cdot 2x}{1}\]\[\lim_{x\rightarrow 4} \frac{\dfrac{x}{(x^2+9)^{1/2}}}{1}\]

Babynini
 one year ago
Best ResponseYou've already chosen the best response.2so for the numerator, does it equal: x^2 + 9  25?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0\[\lim_{x\rightarrow 4} \frac{\dfrac{x}{(x^2+9)^{1/2}}}{1} =\frac{4}{((4)^2+9)^{1/2}} = \color{red}{\frac{4}{5}} \]

Babynini
 one year ago
Best ResponseYou've already chosen the best response.2I'm having trouble with the denominator :

Babynini
 one year ago
Best ResponseYou've already chosen the best response.2@Jhannybean I'm not really sure what all you did because I have no idea how to do derivatives or anything.. so I need to do it algebraically o.o

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Yeah i just realized that, sorry about that

Empty
 one year ago
Best ResponseYou've already chosen the best response.4Yes you're correct with the numerator, however there are two simplifications you can do! combine the 9 and 25 and then you can factor this as the difference of two squares. Try that out, and I'll help you worry about the bottom since you don't want to distribute the bottom actually!

Babynini
 one year ago
Best ResponseYou've already chosen the best response.2Okay! the top then is (x4)(x+4)

Empty
 one year ago
Best ResponseYou've already chosen the best response.4Awesome. Notice anything about the denominator now? :D

Babynini
 one year ago
Best ResponseYou've already chosen the best response.2(Sorry, went to have lunch)

Babynini
 one year ago
Best ResponseYou've already chosen the best response.2\[\frac{ x4 }{ \sqrt{x^2+9} }\]

Babynini
 one year ago
Best ResponseYou've already chosen the best response.2(with a +5 in the denominator, sorry)

Empty
 one year ago
Best ResponseYou've already chosen the best response.4Awesome, now try taking the limit. :P

Babynini
 one year ago
Best ResponseYou've already chosen the best response.2(44)/ [sq{4^2+9)}+5]

Babynini
 one year ago
Best ResponseYou've already chosen the best response.2It's not working! because it ends up being a negative under the sq root..

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.0\(\large\rm 4^2\ne(4)^2\) careful how you square.
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