Question

Use the two-path test to prove that the following limit does not exist. lim (x,y)?(0,0) (y^4 - 2x^2) / (y^4 + x^2) What value does f(x,y) = (y^4 - 2x^2) / (y^4 + x^2) approach as (x,y) approaches (0,0) along the x-axis? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. f(x,y) approaches [ ]. (Simplify your answer.) B. f(x,y) has no limit and does not approach ? or - ? as (x,y) approaches (0,0) along the x-axis. What value does f(x,y) = (y^4 - 2x^2) / (y^4 + x^2) approach as (x,y) approaches (0,0) along the y-axis? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. f(x,y) approaches [ ]. (Simplify your answer.) B. f(x,y) has no limit and does not approach ? or - ? as (x,y) approaches (0,0) along the y-axis. Why does the given limit not exist? A. As (x,y) approaches (0,0) along different paths, f(x,y) always approaches the same value. B. As (x,y) approaches (0,0), the denominator approaches 0. C. As (x,y) approaches (0,0) along different paths, f(x,y) does not always approach a finite value. D. As (x,y) approaches (0,0) along different paths, f(x,y) approaches two different values.

          Use the two-path test to prove that the following limit does not exist.
lim (x,y)?(0,0) (y^4 - 2x^2) / (y^4 + x^2)
What value does f(x,y) = (y^4 - 2x^2) / (y^4 + x^2) approach as (x,y) approaches (0,0) along the x-axis? Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A. f(x,y) approaches [ ]. (Simplify your answer.)
B. f(x,y) has no limit and does not approach ? or - ? as (x,y) approaches (0,0) along the x-axis.
What value does f(x,y) = (y^4 - 2x^2) / (y^4 + x^2) approach as (x,y) approaches (0,0) along the y-axis? Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A. f(x,y) approaches [ ]. (Simplify your answer.)
B. f(x,y) has no limit and does not approach ? or - ? as (x,y) approaches (0,0) along the y-axis.
Why does the given limit not exist?
A. As (x,y) approaches (0,0) along different paths, f(x,y) always approaches the same value.
B. As (x,y) approaches (0,0), the denominator approaches 0.
C. As (x,y) approaches (0,0) along different paths, f(x,y) does not always approach a finite value.
D. As (x,y) approaches (0,0) along different paths, f(x,y) approaches two different values.

Use the two-path test to prove that the following limit does not exist.
lim (x,y)?(0,0) (y^4 - 2x^2) / (y^4 + x^2)
What value does f(x,y) = (y^4 - 2x^2) / (y^4 + x^2) approach as (x,y) approaches (0,0) along the x-axis? Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A. f(x,y) approaches [ ]. (Simplify your answer.)
B. f(x,y) has no limit and does not approach ? or - ? as (x,y) approaches (0,0) along the x-axis.
What value does f(x,y) = (y^4 - 2x^2) / (y^4 + x^2) approach as (x,y) approaches (0,0) along the y-axis? Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A. f(x,y) approaches [ ]. (Simplify your answer.)
B. f(x,y) has no limit and does not approach ? or - ? as (x,y) approaches (0,0) along the y-axis.
Why does the given limit not exist?
A. As (x,y) approaches (0,0) along different paths, f(x,y) always approaches the same value.
B. As (x,y) approaches (0,0), the denominator approaches 0.
C. As (x,y) approaches (0,0) along different paths, f(x,y) does not always approach a finite value.
D. As (x,y) approaches (0,0) along different paths, f(x,y) approaches two different values.

Added by Cynthia M.

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