I am given this limit and am asked to find parameters α and β

$\displaystyle \lim _{x \mapsto 1 } \frac{x^2 + \alpha x + \beta}{x^2 - 1} = 2$

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- Feb 4th 2013, 12:31 PMtheintervurtLimits - find parameters α , β
I am given this limit and am asked to find parameters α and β

$\displaystyle \lim _{x \mapsto 1 } \frac{x^2 + \alpha x + \beta}{x^2 - 1} = 2$ - Feb 4th 2013, 01:03 PMPlatoRe: Limits - find parameters α , β
- Feb 4th 2013, 09:20 PMtheintervurtRe: Limits - find parameters α , β
Thanks, I do understand the reasoning behind this however I am curious is there another way of going about it without having to introduce a new parameter (c) ?

Also here is another similar case which I can't solve

$\displaystyle \lim _{x\mapsto 0} \frac {\gamma + \delta \sin {x}}{x^2} = 3$

again I have to find γ and δ however I haven't been able to figure out how to proceed - Feb 5th 2013, 06:23 AMPlatoRe: Limits - find parameters α , β

First, Never,**never**continue an existing thread with a new question.

**With a new question**always start a new thread.

Now, as written $\displaystyle \lim _{x\mapsto 0} \frac {\gamma + \delta \sin {x}}{x^2} = 3$ has no solution.

If it were $\displaystyle \lim _{x\mapsto 0} \frac {\gamma x + \delta \sin {x}}{x^2} = 3$ there is a solution.

Now, I am absolutely not a fan of using l'Hopital's rule for limits, but in this case it is useful.