This one is tough. "A ballon in the shape of a cylinder with hemispherical ends of the same radius as that of the cylinder is shown. The ballon is being inflated at the rate of 261pi cubic centimeters per minute. At the instant the radius of the cylinder is 3 centimeters, the volume of the ballon is 144pi cubic centimeters and the radius of the cylinder is increasing at the rate of 2 centimeters per minute. At this instant, how fast is the height of the entire ballon increasing?"

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  1. Use Newton's Method to find the root of 2x2+5=ex accurate to six decimal places in the interval [3,4].

    (Note: Answers should be in decimal form. Up to two decimal places only.)

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