[Solution Library] Let f(x)= \begincases-2 x \text if x<0 , 2 x \text if 0 ≤q x<1 , 1/2(x+1)^2 \text if x ≥q 1endcases (v) Is f(x) is continuous at x=0 ?
Question: Let
\(f(x)= \begin{cases}-2 x & \text { if } x<0 \\ 2 x & \text { if } 0 \leq x<1 & \\ \frac{1}{2}(x+1)^{2} & \text { if } x \geq 1\end{cases}\)
(v) Is \(f(x)\) is continuous at \(x=0 ?\)
(vi) Is \(f(x)\) has a derivative at \(x=0 ?\) If so, find thẹ value of it.
(ix) \(\lim _{x \rightarrow 1} f(x)\)
(x) \(f(1)\)
(xi) Is \(f(x)\) is continuous at \(x=1 ?\)
(xii) Is \(f(x)\) has a derivative at \(x=1\) ? If so, find the value of it.
Deliverable: Word Document 
(Solution Library) Find the values of the limits: (b) lim _t \rightarrow-1^+
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