calculus

agam
91.docx

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) = ?