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Find lim(xrarr0)f(x)a n d(lim)(x->1)f(x)...

Find `lim_(xrarr0)f(x)a n d(lim)_(x->1)f(x),w h e r ef(x)={(2x+3, x<=0),(3(x+1),x>0):}`

Text Solution

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we have `f(x)={(2x+3, x<=0),(3(x+1),x>0):}`
For the first case:
`LHL`: `lim_(x->0^-)f(x)=lim_(x->0^-)(2x+3)=2xx0+3=3`
`RHL`:`lim_(x->0^+)f(x)=lim_(x->0^+)3(x+1)=3(0+1)=3`
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