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Assuming, $$f(x)=\frac{x^2-9}{x^2+2x-3},\;\;\;\text{if}\;\;x<-3$$ and $$f(x)=a\sin(\pi x)+b,\;\;\;\text{if}\;\; x\geq-3$$ a and b are some constant find $a$ and $b$ if $f(x)$ is continuous everywhere i use left limit =lright limit to compute it I find that $$a\sin(-3\pi)+b =3/2$$ but it is the final ans?? how can i solve a and b also, the question also ask me :are any a and b can make $f(x)$ differentiable everywhere? how can i prove it is corrent or incorrent,i have no idea about this.

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Your approach -- equating limits -- is correct, but there is something missing in your question. Where did $b$ come from? –  glebovg Dec 10 '12 at 8:11
    
the question said that a and b ar e some constant –  user52477 Dec 10 '12 at 8:12
    
There is not $b$ in the definition of $f$. –  glebovg Dec 10 '12 at 8:13
    
sorry i miss it –  user52477 Dec 10 '12 at 8:14
    
To find $a$ and $b$, evaluate $f$ at some points. –  glebovg Dec 10 '12 at 8:15
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