calculus
Use a linear approximation (or differentials) to estimate the given number. e0.01
calculus
Find the linearization L(x) of the function at a. f(x) = x3/4, a = 81
calculus
A boat is pulled into a dock by a rope attached to the bow of the boat and passing through a pulley on the dock that is 1 m higher than the bow of the boat. If the rope is pulled in at a rate of 1 m/s, how fast is the boat approaching the dock when it is 7 m from the dock? (Ro...
calculus
A street light is mounted at the top of a 15-ft-tall pole. A man 6 ft tall walks away from the pole with a speed of 7 ft/s along a straight path. How fast is the tip of his shadow moving when he is 45 ft from the pole? ft/s
calculus
The radius of a sphere is increasing at a rate of 2 mm/s. How fast is the volume increasing when the diameter is 80 mm? mm^3/s
calculus
A freshly brewed cup of coffee has temperature 95°C in a 20°C room. When its temperature is 68°C, it is cooling at a rate of 1°C per minute. When does this occur? (Round your answer to two decimal places.)
calculus
A sample of a radioactive substance decayed to 94.5% of its original amount after a year. (Round your answers to two decimal places.) (a) What is the half-life of the substance? (b) How long would it take the sample to decay to 65% of its original amount?
calculus
A common inhabitant of human intestines is the bacterium Escherichia coli. A cell of this bacterium in a nutrient-broth medium divides into two cells every 20 minutes. The initial population of a culture is 51 cells. (a) Find the relative growth rate. (Assume t is measured in ...
calculus
Use implicit differentiation to find an equation of the tangent line to the curve at the given point. x2 + 2xy − y2 + x = 17, (3, 5) (hyperbola)
calculus
no its 9 to the power 8 to the power x to the power 2
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