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Apr
16
revised How to determine if an equation represents a cubic spline?
correction
Apr
16
comment How to determine if an equation represents a cubic spline?
@jaska Whoops! LutzL is right! I forgot! You have to check the second derivative too.
Apr
16
comment How to determine if an equation represents a cubic spline?
Yes, the derivatives of both functions should be the same value at x=1. (And the values of the functions should also be the same at x=1.)
Apr
16
comment linear system equation
I think the slope intercept form of both eqns are the same, as they should be. You wrote one equation into the form $y=...$ (i.e. no coefficient in front of $y$). Do the exact same thing for the other eqn and see what you get.
Apr
16
answered How to determine if an equation represents a cubic spline?
Feb
16
asked Error from bias and noise in a linear operator
Feb
6
awarded  Yearling
Jan
19
comment Curvature of a parallel surface
Understood, thanks. The thing is I haven't been able to get this result by going through the mchinery of differential geometry.
Jan
19
asked Curvature of a parallel surface
Nov
25
awarded  Popular Question
Nov
18
awarded  Tumbleweed
Nov
13
answered Finding family of functions for which $\Delta h = 0$
Nov
11
asked How to generalize trace and determinant
Oct
12
comment What is the metric on a cone?
Much obliged! Thanks. Actually, the zero curvature is one of the reasons I picked the cone. I figure if I can go through all the machinations and get to zero, which I knew to be the case ahead of time, then I figure I am doing things right. It all seems to be working out, BTW. Thanks again.
Oct
12
accepted What is the metric on a cone?
Oct
12
asked What is the metric on a cone?
Sep
19
answered How can I calculate a polynomial trend line where `y` always increases as `x` increases?
Sep
18
comment Limit of a function containing square root.
It's someone's creation, maybe someone with authority, but still someone. They created a particular problem for you to solve. It involves $|\sin x|$ simply because the square root sign means "take the positive root". Sure, you can create another problem that would give results as in your second graph, but that's not the problem you are asked to solve. In answer to your question, "But why can't we define ... ?", well, sure, you can. But that's not what the author of the problem did. It's all a matter of meaning: The sqrt symbol means take the positive root.
Sep
18
comment Limit of a function containing square root.
"But why can't we define the function as positive for all the values in the domain?" We can do that, sure. But that is not what the author of your text book has done. The square root symbol simply has the meaning of taking the positive root. It's not that what you want can't be done. It's just that if you do that, you are solving a different problem than the one stated.
Sep
8
answered What does “*the best approximation $A_{a}(x)$ of a function $f(x)$*” mean?