Search results
Results from the WOW.Com Content Network
The first part of this joke relies on the fact that the primitive (formed when finding the antiderivative) of the function 1/x is log().The second part is then based on the fact that the antiderivative is actually a class of functions, requiring the inclusion of a constant of integration, usually denoted as C—something which calculus students may forget.
A lemniscate divided into 15 sections of equal arclength (red curves). Because the prime factors of 15 (3 and 5) are both Fermat primes, this polygon (in black) is constructible using a straightedge and compass. Later mathematicians generalized this result.
For example, from the differential equation definition, e x e −x = 1 when x = 0 and its derivative using the product rule is e x e −x − e x e −x = 0 for all x, so e x e −x = 1 for all x. From any of these definitions it can be shown that the exponential function obeys the basic exponentiation identity.
For instance, rearranging the terms of the alternating harmonic series so that each positive term of the original series is followed by two negative terms of the original series rather than just one yields [34] + + + = + + + = + + + = (+ + +), which is times the original series, so it would have a sum of half of the natural logarithm of 2. By ...
36.24 6 3 1 Below normal 1852: 73.28 5 5 1 Near normal 1853: 76.49 8 4 2 Near normal 1854: 31.00 5 3 1 Below normal 1855: 18.12 5 4 1 Below normal 1856: 48.94 6 4 2 Below normal 1857: 46.84 4 3 0 Below normal 1858: 44.79 6 6 0 Below normal 1859: 55.73 8 7 1 Below normal 1860: 62.06 7 6 1 Below normal 1861: 49.71 8 6 0 Below normal 1862: 46.03 6 ...