Hi,
can somebody help me with this? The textbook doesn't give any good examples on how to solve these.
lim as (x,y,z) --> (0,0,0) for (x^2+2y^2+3z^2)/(x^2+y^2+z^2)
can somebody help me with this? The textbook doesn't give any good examples on how to solve these.
lim as (x,y,z) --> (0,0,0) for (x^2+2y^2+3z^2)/(x^2+y^2+z^2)
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You have continuous partial derivatives all around (but not at) the origin, so the limit will exist if each of the single-variable limits exist and have the same value:
lim/x->0 f(x, 0, 0) = lim x^2 / x^2 = 1
lim/y->0 f(0, y, 0) = (2y^2) / y^2 = 2
lim/z->0 f(0, 0, z) = (3z^2) / z^2 = 3
Approaching (0,0,0) from three different directions gives different results, so the limit does not exist.
lim/x->0 f(x, 0, 0) = lim x^2 / x^2 = 1
lim/y->0 f(0, y, 0) = (2y^2) / y^2 = 2
lim/z->0 f(0, 0, z) = (3z^2) / z^2 = 3
Approaching (0,0,0) from three different directions gives different results, so the limit does not exist.
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x-> 0 then y-> 0 then z-> 0
Ans
3
Ans
3