Question

Question 23- of 40 Step 1 of 1 01:42:27 Use the epsilon-delta definition to find lim TV) + (400) 4 - 4x? - 8y? Write the exact answer. Do not round. If the limit does not exist, write DNE for x² + 2y your answer. 2 Points Keypad Keyboard Shortcuts IF < > In = VI 2 log RCA V e λμ ( ) sec cot) cot") e SCC

Answer 1

$$The correct answer is \textbf{DNE}.\\ \\That is, the limit do not exist. \\\\Note that the given limit can be expressed as$\;\;\lim_{(x,y)\to (0,0)}\;\left(-4+\frac{x^{4}}{x^{2}+2y^{2}}\right)\;$\\ \\Note that the limit depends on the path along which $\;(x,y)\;$ approaches to $\;(0,0)\;.\;$\\ \\For example, when $\;(x,y)\;$ approaches to $\;(0,0)\;$ along the x -axis,\\ the limit becomes $\;0\;.\;$\\ \\ when $\;(x,y)\;$ approaches to $\;(0,0)\;$ along the y -axis ,\\ the limit becomes $\;\infty\;.\;$\\$