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f(x) = 5x -4, when 0<x<=1, 4x^2-3x when ...

`f(x) = 5x -4, when 0

Text Solution

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LHS
`lim_(x->1^-)f(x)=lim_(x->1^-)(5x-4)`
`=lim_(h->0)(5(1-h)-4)`
`=5-4=1`
RHS
`=lim_(x->1^+)f(x)=lim_(h->1^-)(4(1+h)^2-3(1+h))`
`=lim_(h->0)(4(1+h^2+2h)-3-3h)`
`=4(1+0)-3-0=1`
...
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