Evaluate $\lim _ { ( x , y ) \rightarrow ( 2,2 ) } \frac { \tan \left( ( x - 2 ) ^ { 2 } + ( y - 2 ) ^ { 2 } \right) } { ( x - 2 ) ^ { 2 } + ( y - 2 ) ^ { 2 } }$
A)0
B)1
C)2
D)3
E)4
F)5
G)6
H)Does not exist

Question

Evaluate $\lim _ { ( x , y ) \rightarrow ( 2,2 ) } \frac { \tan \left( ( x - 2 ) ^ { 2 } + ( y - 2 ) ^ { 2 } \right) } { ( x - 2 ) ^ { 2 } + ( y - 2 ) ^ { 2 } }$ 
A)0
B)1
C)2
D)3
E)4
F)5
G)6
H)Does not exist

Quizplus · Accepted Answer

The limit evaluates to 1 because it is of the form $\frac{\tan(z)}{z}$ as $z \rightarrow 0$, where $z = (x - 2)^2 + (y - 2)^2$. This is a standard limit in calculus, known to approach 1 as $z$ approaches 0.

Evaluate A)0 B)1 C)2 D)3 E)4 F)5 G)6 H)Does Not Exist

Evaluate A)0
B)1
C)2
D)3
E)4
F)5
G)6
H)Does Not Exist