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Homework Statement 1. Write an interval formula for the solution f'(x)=2f(x)+e^x f(1)=0 Explicitly find the maximal interval I about 0 on which we can solve the following differential equations 2. f'(x) = xf(x) f(0)=1 3. f'(x)=[f(x)]^2 f(0)=-1 Homework Equations For...

Yes, I see what you mean. Thank you. Does anyone know how to close or edit the words "SOLVED" in threads?

Homework Statement Which subset of R are both sequentially compact and connected? Homework Equations The Attempt at a Solution The connected subsets of R are the empty set, points, and intervals. The subsets of R that are compact are closed and bounded. Thus, the subsets of...

If |b| is fixed at 1, then a dot b = |a| cos(theta). cos(theta) = 1, since a is in the direction of b. So, we get a dot b = |a| = \sqrt{1^2+2^2+3^2} = \sqrt{14} I finally understood what you meant by Thank you very much for your help. Cheers.

Hm, ok. So if the magnitude of the vector is 1, then the maximum value of this dot product would be 1(1) + 2(1) + 3(1) = 6 since the points are nonzero, correct?

Ah, ok. So, I'm supposed to find the directional derivative of f at (1,2,3) in the direction of a = (x,y,z) 1. Let a be a nonzero vector, where I am trying to find the directional derivatie of f at (x,y,z) in the direction of a \left\| a \right\| = \sqrt{1^2+2^2+3^2} = \sqrt{14} 2. So, the...

Homework Statement Find the maximum of \frac{x+2y+3z}{\sqrt{x^2+y^2+z^2}} as (x,y,z) varies among nonzero points in R^{3} Homework Equations I'm not sure. The section in which this problem lies in talks about scalar products, norms, distances of vectors, and orthognality. However, I...