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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.
Objectives : After studying this unit, you should be able to : 1. explain the processes involved in counting; 2. explain why the ability to recite number names is no in
David wants to rent a movie. He wants to watch either a comedy or a drama. The movie rental store has 18 comedies and dramas available for rent. Seven of the movies are comedies, a
Suppose that x = x (t ) and y = y (t ) and differentiate the following equation with respect to t. Solution x 3 y 6 + e 1- x - cos (5
Standard form of the line Let's begin this section off along a quick mathematical definition of a line. Any equation that can be written in the following form,
Determine how many different words can be formed out of the letters of the word VARANASI? Ans: 720 different words can be formed out of the letters of the word VARANASI.
IN THIS WE HAVE TO ADD THE PROBABILITY of 3 and 5 occuring separtely and subtract prob. of 3 and 5 occuring together therefore p=(166+100-33)/500=233/500=0.466
Construction of indirect tangents
how to get the objective report?
Find the number of zeros of the polynomial from the graph given. (Ans:1)
You plan to retire when you are 65th years old. You are now 25 years old. You plan to buy a pension annuity that will pay you $100,000 per year starting one year after you turn 6
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