Calculus and its Applications by P. Mainardi and H. Barkan (Auth.)

By P. Mainardi and H. Barkan (Auth.)

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14 35 n e t w o r t h s ever t h e same? 9« 10« If sin 0 and cos 0 are both kncwn to vary continuously with 0, what can be said about the continuity of tan 0? If sin 0 is known to be a single-valued continuous function for which sin 0 • 0 and sin £ - i f w hat can one say about sin 0 for 0 < 0 < ^ ? 11. The saleable amount of a spoiling crop is reducing continuously at the same time that its market price per unit is advancing continuously. What can be said about the value of the crop at any time?

Where y is the total profit derived from the sale of x units of a certain article. where w is the weight of an individual at a given time and h is his height at the same time. 5. Show that for the function y • mx • b the average rate of change of y with respect to x is independent of the size of the interval considered. 6. Show that foir the function defined by - + Z » 1 the a D average rate of change of x with respect to y is independent of the size of the interval considered. 7# Explain verbally or with appropriately defined symbols the meaning of the following statements.

Our approximation, in this case, was correct to five decimal places. Consider the air pressure y at elevation x above sea level to be given by r - aiooe" 0 000 0 3 7 x . , to find the instantaneous rate of change of pressure with respect to the elevation. We shall proceed as before, forming the difference quotient for the interval from x^tox-^ + A X : rf As before we shall attempt to find the "target value which §J approaches? , lim Ax-*- 0 ^ when x - . 1 The student will readily recognize that the finding of the limit in this case «is not nearly as simple as in the previous example.

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