Let the voltage in a circuit be described by = for current and resistance .

A. Find an equation of a plane tangent to V = /R to approximate voltage for values of current near 0.04 amps and resistance 600 ohms. B. Use the Linearization to approximate voltage when the current 0.041 amps and resistance 603 ohms. C. The voltage drops as the battery in the circuit wears out. Voltage V, current I, and resistance R are all functions of time. Write the correct Chain Rule to calculate the rate of change of current with respect to time. D. Calculate the rate of change of current with respect to time at the instant when R = 600 ohms, / = 0.04 amps, - = 0.5 ohms / sec, -= -0.01 volt / sec. E. Write an equation to approximate the maximum error calculating current based on measurements for voltage I and resistance R with measurement errors dl and dR. F. Find an interval for acceptable current calculations given measurements for voltage 24 volts and resistance 600 ohms with measurement errors 1 volt and 5 ohms respectively