Jin L.
asked • 02/03/23(x,y)-->(0,0) ((x^4)(y^3))/(x^10 + y^5) along the path y=kx^2
I have no idea how to solve this. I know you must plug in the given path and see but a little I'm lost. What values do the limit exist? What values does the limit not exist? When I solve it on my own I just get 0 and I'm not sure how to get values for limit exists or not exists.
Dayv O. answered • 02/03/23
Caring Super Enthusiastic Knowledgeable Calculus Tutor
when y=kx2 is used in f(x,y) above
then f(x,kx2)=k3x10/((1+k5)x10)
which if x->0 approaches(remains at) k3/(1+k5)
Yefim S. answered • 02/03/23
Math Tutor with Experience
lim (x, y) → (0, 0) (x4y3)/(x10 + y5) = lim (x, kx2) x→0 (k3x10)/(x10 + k5x10) = k3/(1 + k5)
Jin L.
My answer options are: (A). [k^3/(1+k^5) if k ≠ -1, DNE if k = -1] (B). [k^3/(1+k^5) if k ≠ 0, DNE if k=0] (C) [0 if k≠-1, DNE if k =-1] (D). [0 for all k in R] (E). [infinity for all k in R] What is the correct one? I think it is A or C because when plugging in -1 it becomes undefined?02/03/23
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Jin L.
My answer options are: (A). [k^3/(1+k^5) if k ≠ -1, DNE if k = -1] (B). [k^3/(1+k^5) if k ≠ 0, DNE if k=0] (C) [0 if k≠-1, DNE if k =-1] (D). [0 for all k in R] (E). [infinity for all k in R] which one would it be? plugging in -1 for k gives undefined which would mean it DNE right? so would it be (A) ?02/03/23