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The function is $\"f(x)=\\frac{x^2+x}{\\sqrt{x^3+x^2}}\"$ .

Graph :

Graph of the function $\"f(x)=\\frac{x^2+x}{\\sqrt{x^3+x^2}}\"$ :

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(a)

Find $\"\\lim_{x\\rightarrow0^-}f(x)\"$ .

Observe the above graph.

As $\"x\"$ tends to $\"0\"$ from left side, $\"f(x)\"$ approaches to $\"-1\"$ .

So $\"\\lim_{x\\rightarrow0^-}f(x)=-1\"$ .

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(b)

Find $\"\\small$ .

Observe the above graph.

As $\"x\"$ tends to $\"0\"$ from right side, $\"f(x)\"$ approaches to $\"1\"$ .

So $\"\\small$ .

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(c)

Find $\"\\small$ .

Left hand limit $\"\\lim_{x\\rightarrow0^-}f(x)=-1\"$ .

Right hand limit $\"\\small$ .

Left hand limit and right hand limit are not equal.

$\"\\small$ does not exist.

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(a) $\"\\lim_{x\\rightarrow0^-}f(x)=-1\"$ .

(b) $\"\\small$ .