Description
Catalog of Functions Students will be required to build a (digital) encyclopedia cataloging some of the many important functions that are encountered in calculus. Each function should be identified by name, formula, and graph, and should also include important information about the function such as domain, range, and how the function is applied in “real life”. The catalog is to be submitted electronically and will be due upon completion of the semester. Progress checks will conducted periodically throughout the semester. the source must be calculus volume 1 derivatives, limits and fractions functions all from volume one calculus Function Eportfolio – Travis KelmThe Natural Logarithm FunctionNotation: The Natural Logarithm Function is denoted by ln(x)
Domain: All positive numbers or ( 0 , ∞ )
Range: All numbers or ( -∞ , ∞ )
Related Functions:
ln(x) is the inverse function to the exponential function ex.
ln(x) is a member of the infinite family of all logarithm functions such
as log2(x), log10(x), log44(x), and so on.
Derivative Function: The derivative function of ln(x) is the reciprocal function 1/x
Why this function is important in the “Real World”: The natural logarithm functions (and
logarithms in general) are useful for solving equations in which the variable occurs in the
exponent.
For example, the equation 5x = 100 is impossible to solve exactly without the use of
logarithms
Equations such as 5x = 100 come up in applications such as finance and biology. For
example, if a population grows at a rate of 30% per year, then the number of years for the
population to double in size is the solution to the equation
1.3x = 2
Since the variable occurs in the exponent, logarithms are necessary to find exact solutions
to such the equation.Function Eportfolio – Travis KelmExponential Function base eNotation: The Natural Logarithm Function is denoted by exDomain: All numbers or ( -∞ , ∞ )
Range: All positive numbers or ( 0 , ∞ )
Related Functions:ex is the inverse function to the natural logarithm function ln(x).ex is a member of the infinite family of all exponential functions such
as ex , 2x , (½)x , and so on.
Derivative Function: The function of ex has the remarkable property that it is equal to its
own derivative, that is, ddxex = ex .
Why this function is important in the “Real World”: Exponential functions such ex are
exceptionally useful for problems that involve exponential growth or decay. ex comes up in
particular when interest is compounded continuously
For example, if you invest $100 in an account that yields 5% annual interest compounded
continuously, then the amount you will have after x years is given by the functionA(x) = 100 (e0.05x)Function Eportfolio – Travis KelmNow you make pages just like the
two examples above for about 18
more functions!
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