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06:29Resistors connected in parallel If two resistors of R₁ and R₂ ohms are connected in parallel in an electric circuit to make an R-ohm resistor, the value of R can be found from the equation
1/R = 1/R₁ + 1/R₂
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If R₁ is decreasing at the rate of 1ohm/sec and R₂ is increasing at the rate of 0.5 ohm/sec, at what rate is R changing when R₁ = 75 ohms and R₂ = 50 ohms?
Find the linearizations of
a. tan x at x = -π/4
Graph the curves and linearizations together.
Right circular cone The lateral surface area S of a right circular cone is related to the base radius r and height h by the equation
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S = πr √ r² + h².
c. How is dS/dt related to dr/dt and dh/dt if neither r nor h is constant?
The lateral surface area S of a right circular cone is related to the base radius r and height h by the equation S = πr√(r² + h²).
a. How is dS/dt related to dr/dt if h is constant?
Find the linearization of ƒ(x) = √(1 + x) + sin x - 0.5 at x = 0.
Moving searchlight beam The figure shows a boat 1 km offshore, sweeping the shore with a searchlight. The light turns at a constant rate, dθ/dt = -0.6 rad/sec.
b. How many revolutions per minute is 0.6 rad/sec?
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