Mastering Limits with L'Hopital's Rule and Factoring Tricks | Homework Help

[Loststudent22]

Homework Statement

$\lim_{\alpha\to\omega}-\frac{\alpha r_0}{\omega(\omega^{2}-\alpha^{2})}\sin(\omega t)+\frac{r_0}{\omega^{2}-\alpha^{2}}\sin(\alpha t)$

Homework Equations

I feel I will need to use fact $\frac{d}{d\omega}\sin(\omega t)=t\cos(\omega t)$

The Attempt at a Solution

[/B]
Nope not sure how to start this one I'm rusty on limitis as it is and basic idea of trying l hopitals rule or factoring tricks are not working. Thanks for any help

 

[Ray Vickson]

Homework Statement

$\lim_{\alpha\to\omega}-\frac{\alpha r_0}{\omega(\omega^{2}-\alpha^{2})}\sin(\omega t)+\frac{r_0}{\omega^{2}-\alpha^{2}}\sin(\alpha t)$

Homework Equations

I feel I will need to use fact $\frac{d}{d\omega}\sin(\omega t)=t\cos(\omega t)$

The Attempt at a Solution

[/B]
Nope not sure how to start this one I'm rusty on limitis as it is and basic idea of trying l hopitals rule or factoring tricks are not working.Thanks for any help

Show us what you did, so we can point out if you made some errors. (Hint: you must have made some.)

 

[Loststudent22]

Show us what you did, so we can point out if you made some errors. (Hint: you must have made some.)

Yeah I need a hint how to even approach this limit because my calculus 1 techniques are not really going anywhere

 

[Ray Vickson]

Yeah I need a hint how to even approach this limit because my calculus 1 techniques are not really going anywhere

Show us the calculus 1 techniques you used, so we can see why you say they are not going anywhere.