Find the limit as x approaches 4. [sqrt(x^2-1)-sqrt(15)]/(x-4)

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Find the limit as x approaches 4. [sqrt(x^2-1)-sqrt(15)]/(x-4)

Mathematics
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|dw:1327298260320:dw|
I drew it to clarify
Lhopital rule. Derivative of top and bottom.

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Could you show me how to find the derivative?
(1/2)(x^2 - 1)^(-1/2) * 2x
chain rule for the first one
bottom basically turns to 1 because you have the variable to the first power and plus or minus a constant
The top should be rewritten to (x^2 - 1)^(1/2) - (15)^(1/2) The constant(15^1/2) turns into a zero. So you're left only doing (x^2 - 1)^(1/2). Drop the power so you get (1/2)(x^2 -1 )^(-1/2) Then you do chain rule. Derive the inside you end up getting (x)(x^2 -1)^(-1/2) |dw:1327298668258:dw|
Forgot about the limit part. Basically you just plug 4 back in there. |dw:1327298727681:dw|
snakefangs thanks for the insight, but we haven't even gotten into the chapter about derivatives and the chain rule yet, im just having trouble getting this out of indeterminant form.
Ah... sorry about that then I'll try and see if i can apply some algebraic method.

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