Calculus

Calculus

QUESTION

1. A minivan was purchased for $32,000. If the value of the minivan depreciates by $1,700 per year, find a linear function that models the value V of the car after t years. Use the function and find the value of the car after 5 years.

2. Simplify tan x(csc x – sin x)

3. 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(t)

, of the bacteria as a function of time, and find the approximate area of the bacterial culture in 4 hours.

4. A pendulum moving in simple harmonic motion is modelled by the functions open parentheses t close parentheses equals negative 5 cos left parenthesis begin inline style fraction numerator pi t over denominator 4 end fraction end style right parenthesis, where s is measured in inches and t is measured in seconds. Determine the first time when the distance moved is 4 inches.

5. Solve 2 log subscript 5 open parentheses square root of x close parentheses minus log subscript 5 open parentheses 6 x minus 1 close parentheses equals 0.

6. Estimate the slope of the tangent line to f open parentheses x close parentheses equals x cubed at x =2 by finding the slope of the secant line through (2,f(2))  and (2.001,f(2.001))

CLOSE
CLOSE