Evaluate the limit

lim x (5-x)(5+4x)/(3-5x)(9+6x)

Evaluate the limit

lim x . 10x^3-11x^2-9x/9-10x-10x3

Water is leaking out of an inverted conical tank at a rate of 12100 cubic centimeters per min at the same time that water is being pumped into the tank at a constant rate. The tank has height 13 meters and the diameter at the top is 5 meters. If the water level is rising at a rate of 27 centimeters per minute when the height of the water is 2.5 meters, find the rate at which water is being pumped into the tank in cubic centimeters per minute.

When air expands adiabatically (without gaining or losing heat), its pressure P and volume V are related by the equation PV1.4= C where C is a constant. Suppose that at a certain instant the volume is 660 cubic centimeters and the pressure is 91kPa and is decreasing at a rate of 8kPa/minute. At what rate in cubic centimeters per minute is the volume increasing at this instant? cm 3 min (Pa stands for Pascal -- it is equivalent to one Newton/(meter squared); kPa is a kiloPascal or 1000 Pascals. )

A street light is at the top of a 19 ft tall pole. A woman 6 ft tall walks away from the pole with a speed of 5 ft/sec along a straight path. How fast is the tip of her shadow moving when she is 50 ft from the base of the pole?

Let y=sin(4x). If x = 0.2 at x=0, use linear approximation to estimate yy = Find the percentage error

error = %

Use linear approximation to estimate the amount of paint in cubic centimeters needed to apply a coat of paint 0.03cm thick to a hemispherical dome with a diameter of 55 meters.