calculus

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1. (9)

Consider the function f left parenthesis x right parenthesisshown 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) = ?