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(Solved): answer a & c !! 3. (10 pts each) Let \( D=\{(t, y): t \in[0,1], y \in[0,1]\} \). Consider \[ f(t ...
answer a & c !!
![3. (10 pts each) Let \( D=\{(t, y): t \in[0,1], y \in[0,1]\} \). Consider
\[
f(t, y)=\frac{t}{1+y^{2}} .
\]
a. Prove that \(](https://media.cheggcdn.com/study/e92/e9216523-4699-4946-9ece-c3342d2e93c9/image)
3. (10 pts each) Let \( D=\{(t, y): t \in[0,1], y \in[0,1]\} \). Consider \[ f(t, y)=\frac{t}{1+y^{2}} . \] a. Prove that \( D \) is convex. b. Prove that \( f \) satisfies the Lipschitz condition on \( D \). c. Prove that the differential system \[ y^{\prime}(t)=\frac{t}{1+y^{2}}, \quad y(0)=1, \]
Expert Answer
A set S is said to be convex iff the convex linear combination of any two points of set S a belongs to S. That i