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if f(x) = {{:(x+2",",xle1),(cx^(2)",",xg...

if `f(x) = {{:(x+2",",xle1),(cx^(2)",",xgt-1):},` then find c when `lim(xto-1)f(x)` exists.

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Given, `f(x) = {{:(x+2",",xle1),(cx^(2)",",xgt-1):},`
LHL=`lim_(xto-1^(-))f(x)= underset(xto-1^(-1))"lim"(x+2)`
`=lim_(hto0)(-1-h+2)=lim_(hto0)(1-h)=1`
RHL `=lim_(xto-1^(+))f(x)= lim_(xto-1^(+)) cx^(2)=lim_(hto0)c(-1+h)^(2)`
`therefore` = c
If `lim_(xto-1)f(x)` exist, then LHL = RHL
`therefore c=1`
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