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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 probability that an account officer will pass her exam is 5/9. if she pass,the probability that she will be promoted is 3/4. she is not promoted if she fails her professional e
y(x) = x -3/2 is a solution to 4x 2 y′′ + 12xy′ + 3y = 0 , y (4) = 1/8 , and y'(4) = -3/64 Solution : As we noticed in previous illustration the function is a solution an
-x^3+6x-7
what is the quotient of 3 and n?
16 times 4
A word on an alphabet is any arrangement of the letters in the alphabet. For example,ODD, DOD, DOO, DDD are three-letter words on the alphabet {D,O}. How many four-letter words are
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A painter leans a 10-foot ladder against the house she is to paint. The foot of the ladder is 3 feet from the house. How far above the ground does the ladder touch the house? Appro
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