Show That the Limit $\lim _ { ( x , y ) \rightarrow ( 0,0 ) } \frac { 2 x ^ { 2 } - y ^ { 2 } } { x ^ { 2 } + 2 y ^ { 2 } }$

question 109

Essay

Show that the limit $\lim _ { ( x , y ) \rightarrow ( 0,0 ) } \frac { 2 x ^ { 2 } - y ^ { 2 } } { x ^ { 2 } + 2 y ^ { 2 } }$ does not exist.

---

Definitions:

Embryonic Stage

A critical phase of prenatal development that spans from implantation of the zygote in the uterine wall through the eighth week, where major organs and structures begin to form.

Zygote

A fertilized ovum (egg cell).

Uterine Wall

The muscular wall of the uterus, which thickens during the menstrual cycle and pregnancy, playing a key role in pregnancy and childbirth.

Fetus

A developing mammal or human from the ninth week after conception until birth.