Use Polar Coordinates to Find the Limit of the Function $$f ( x , y ) = \cos \left( \frac { x ^ { 2 } } { x ^ { 2 } + y ^ { 2 } } \right)$$

question 263

Multiple Choice

Use polar coordinates to find the limit of the function as (x, y) approaches (0, 0) .
- $$f ( x , y ) = \cos \left( \frac { x ^ { 2 } } { x ^ { 2 } + y ^ { 2 } } \right)$$

• A) 1
• B) \(\frac { \pi } { 2 }\)
• C) 0
• D) No limit

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Definitions:

Osteoarthritis

A degenerative joint disease characterized by the breakdown and eventual loss of the cartilage of one or more joints, leading to pain and stiffness.

Diaphysis

The main or midsection (shaft) of a long bone, which is typically cylindrical in shape and contains the bone marrow.

Epiphysis

The end part of a long bone, initially growing separately from the shaft and later fusing to form mature bone.

Periosteum

A dense layer of vascular connective tissue enveloping the bones except at the surfaces of the joints.