Change order between integral and differential calculation

micheal9000
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Please help look at this picture and give me the answer please: are those right or not? In general look, when we can change the order between integral and differential calculation?https://m.ak.fbcdn.net/sphotos-h.ak/hphotos-ak-xpf1/v/t34.0-12/10603742_848540828497240_5787805822965408581_n.jpg?oh=d1301631ee463def5808c00a56f64db7&oe=541CA6B5&__gda__=1411157002_20c5d665996e10a1d77440ee28d0618b
 
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I can see no picture.
 
Thread 'Direction Fields and Isoclines'

Thread 'Direction Fields and Isoclines'

I sketched the isoclines for $$ m=-1,0,1,2 $$. Since both $$ \frac{dy}{dx} $$ and $$ D_{y} \frac{dy}{dx} $$ are continuous on the square region R defined by $$ -4\leq x \leq 4, -4 \leq y \leq 4 $$ the existence and uniqueness theorem guarantees that if we pick a point in the interior that lies on an isocline there will be a unique differentiable function (solution) passing through that point. I understand that a solution exists but I unsure how to actually sketch it. For example, consider a...
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