1. (9)
Consider the function f left parenthesis x right parenthesis
shown in the following image:
Midterm q9 graph
Evaluate limit as x rightwards arrow 0 to the power of minus of space f left parenthesis x right parenthesis
.
Multiple choices
A. -1
B. 0
C. 1
D. Does not exist
2.
A research lab grows a type of bacterium in culture in a circular region. The radius of the circle, measured in centimeters, is given by begin mathsize 12px style r left parenthesis t right parenthesis space equals space 5 space minus space fraction numerator 6 over denominator t squared plus 3 end fraction end style
, where t
is time measured in hours passed since a circle of a 1cm radius of the bacterium was put into the culture. Express the area,
A open parentheses t close parentheses
, of the bacteria as a function of time, and find the approximate area of the bacterial culture in 4 hours.
A(t) = ?