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Exponential Functions : We'll begin by looking at the exponential function,
f ( x ) = a x
We desire to differentiate this. The power rule which we looked previous section won't work as which required the exponent to be a fixed number & the base to be a variable. That is accurately the opposite from what we've got with this function. Thus, we're going to have to begin with the definition of the derivative.
Now, the a x is not influenced by the limit as it doesn't have any h's in it and hence is a constant so far as the limit is concerned. Therefore we can factor this out of the limit. It specified,
Now let's notice as well that the limit we've got above is accurately the definition of the derivative of f ( x ) = a x at x = 0 , i.e. f ′ (0) . Thus, the derivative becomes,
f ′ ( x ) = f ′ (0)a x
Thus, we are type of stuck. We have to know the derivative to get the derivative!
There is one value of a that we can deal along with at this point. There are actually a variety of ways to define e. Following are three of them.
the sum of the vector QR, -SR, TQ and 2ST is?
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Question: Let f be a quartic polynomial (ie. a polynomial of degree 4). Suppose that f has zeros at -2; 1; 3; 4 and that f(0) = 4. Sketch a graph of f. If f(x) is
How do get help with my work? should i just type it in this box...? sorry thanks!
Let's start things by searching for a mixing problem. Previously we saw these were back in the first order section. In those problems we had a tank of liquid with several kinds of
Determine or find out if the subsequent series is convergent or divergent. If it converges find out its value. Solution To find out if the series is convergent we fir
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The frequency of oscillation of an object suspended on a spring depends on the stiffness k of the spring (called the spring constant) and the mass m of the object. If the spring is
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