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Definition : A function f ( x ) is called differentiable at x = a if f ′ ( x ) exists & f ( x ) is called differentiable onto an interval if the derivative present for each of the point in that interval.
The next theorem illustrates us a very nice relationship among functions which are continuous & those that are differentiable.
Theorem: If f ( x ) is differentiable at x = a then f ( x ) is continuous at the point x = a.
Note as well that this theorem does not work in reverse order . Assume f ( x ) = |x| and take a look at,
So,f ( x ) = xis continuous at x =0 to sketch the graph of a function.
Question Solve the following functions for x (where x is a real number). Leave your answers in exact form, that is, do not use a calculator, show all working. (a) 3 x 3 x2 3
First, see that the right hand side of equation (2) is a polynomial and thus continuous. This implies that this can only change sign if this firstly goes by zero. Therefore, if the
what are these all about and could i have some examples of them please
solve for x and y 2x+3y=12 and 30x+11y=112
how to prove Decidability Theorem of Logic
Another aid that can help children practise subtraction is the number strip. TGS can be used to improve their ability to count backwards. For example, subtracting 4 from 9 means
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a3-a2+a-1
Inflation The inflation rate for a given period can be calculated using the following formula; Inflation = (current retail price index/retail price index in the base year)
What are the factors of 956
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