If `f(x)={{:(x-1", "xge1),(2x^(2)-2", "xlt1):},g(x)={{:(x+1", "xgt0),(-x^(2)+1", "xle0):}," and "` `h(x)=|x|," then "lim_(xto0) f(g(h(x)))" is"`______

Question

If `f(x)={{:(x-1", "xge1),(2x^(2)-2", "xlt1):},g(x)={{:(x+1", "xgt0),(-x^(2)+1", "xle0):}," and "` `h(x)=|x|," then "lim_(xto0) f(g(h(x)))" is"`______

If `f(x)={{:(x-1", "xge1),(2x^(2)-2", "xlt1):},g(x)={{:(x+1", "xgt0),(-x^(2)+1", "xle0):}," and "`
`h(x)=|x|," then "lim_(xto0) f(g(h(x)))" is"`_______.

Monjur Alahi

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2025-01-04 04:42

1 Answers

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Salim Ahmed Kawsar · Accepted Answer · 2023-02-05T15:29:48+06:00

Salim Ahmed Kawsar

Correct Answer - `(0)`
`underset(xto0^(+))limf(g(h(x)))=f(g(0^(+)))=f(1^(+))=0`
`underset(xto0^(-))limf(g(h(x)))=f(g(0^(+)))=f(1^(+))=0`
Hence, `underset(xto0)limf(g(h(x)))=0`

4 views Answered 2023-02-05 15:29