Question

Why is ( 1/√[3]x^5 ) undefined when ( x = 0 ) but not when ( x < 0 ) or ( x > 0 )?

a) Because division by zero is undefined.
b) It is defined for all values of ( x ).
c) The expression is only undefined when ( x < 0 ).
d) The expression is only undefined when ( x > 0 ).

Answer 1

The expression (1/√[3]x^5) is undefined when x = 0 because division by zero is undefined. When x < 0 or x > 0, the expression is defined.

Step-by-step explanation:

The expression (1/√[3]x^5) is undefined when x = 0 because division by zero is undefined. When x < 0 or x > 0, the expression is defined.

This can be understood by considering the function y = 1/x. When x approaches zero, y approaches infinity, and as x approaches infinity, y approaches zero. This behavior is known as an asymptote. Since the expression is equivalent to 1/x^5, it will also have a vertical asymptote at x = 0.