Modeling with Rational and Piecewise-Defined Functions: Part Two — Test
Question 22 • Precalculus
Which statement correctly explains whether tis limit exists? limit x to 3 of g times x
Answer
A
The limits limit x to 3 raised to the negative power of g times x is equal to negative 1 point 6 and limit x to 3 raised to the plus power of g times x is equal to 1 point 6 . Both limit x to 3 raised to the negative power of g times x and limit x to 3 raised to the plus power of g times x exist, so limit x to 3 of g times x exists.
B
The limits limit x to 3 raised to the negative power of g times x is equal to negative 1 point 6 and limit x to 3 raised to the plus power of g times x is equal to 1 point 6 . Because limit x to 3 raised to the negative power of g times x is not equal to limit x to 3 raised to the plus power of g times x , limit x to 3 to the th power of g times x does not exist.
C
The limits limit x to 3 raised to the negative power of g times x is equal to 1 point 6 and limit x to 3 raised to the plus power of g times x is equal to negative 1 point 6 . Because limit x to 3 raised to the negative power of g times x is not equal to limit x to 3 raised to the plus power of g times x , limit x to 3 to the th power of g times x does not exist.
D
The limits limit x to 3 raised to the negative power of g times x is equal to 1 point 6 and limit x to 3 raised to the plus power of g times x is equal to negative 1 point 6 . Both limit x to 3 raised to the negative power of g times x and limit x to 3 raised to the plus power of g times x exist, so limit x to 3 to the th power of g times x exists.