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Definition of Natural exponential function: The natural exponential function is f( x ) = ex where, e= 2.71828182845905........ .
Hence, since e > 1 we also know that ex → ∞ as x → ∞ & ex → 0 as x → -∞ .
Graph for the Sequence First we wish to think about the term graphing a sequence. To graph the sequence {a n } we plot the points {n, a n } as n ranges over every possible valu
A standard deck of cards contains 52 cards. One card is selected at random. Determine a) The probability that the card is a 8 or an Ace? b) The probability that the card is
6 male students and 3 female students sit around a round table. The probability that no 2 female students sit beside each other can be expressed as a/b, where a and b are coprime p
If z=re i ? ,find the value of |e iz | Solution) z=r(cos1+isin1) |e iz |=|e ir(cos1+isin1) |=|e -rsin1 |=e -rsin1
More Optimization Problems Example A window is being built in which the bottom is rectangle and the top is a semicircle. If there framing materials is 12 meters what have
the base b of a triangle increases at the rate of 2cm per second, and height h decreases at the rate of 1/2 cm per second. Find rate of change of its area when the base and height
Problem: A person has 3 units of money available for investment in a business opportunity that matures in 1 year. The opportunity is risky in that the return is either double o
INTRODUCTION : We are often confronted with children not being able to deal with H T 0, i.e. 'hundreds', 'tens' and 'ones' (or 'units'), with comfort, though they are supposed to
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A vessel in shape of a inverted cone is surmounted by a cylinder has a common radius of 7cm this was filled with liquid till it covered one third the height of the cylinder. If the
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