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The Definition of the Derivative : In the previous section we saw that the calculation of the slope of a tangent line, the instantaneous rate of change of a function, and the instantaneous velocity of object at x =a all needed us to calculate the following limit.
We also saw that along with a small change of notation this limit could also be written like this,
This is such significant limit and it arises in so several places that we give it a name. We call it a derivative. Following is the official definition of the derivative.
Definition : The derivative of f ( x ) w.r.t. x is the function f ′ ( x ) and is described as,
Note as well that we replaced all the a's in (1) along with x's to acknowledge the fact that the derivative is actually a function as well. We frequently "read" f ′ ( x ) as "f prime of x".
A painting was purchased 11 years ago for $26900. It has just been sold for $78000. Calculate the flat rate of appreciation p.a.
Evaluate the given limit. Solution : It is a combination of many of the functions listed above and none of the limited are violated so all we have to do is plug in x = 3
If α & ß are the zeroes of the polynomial 2x 2 - 4x + 5, then find the value of a.α 2 + ß 2 b. 1/ α + 1/ ß c. (α - ß) 2 d. 1/α 2 + 1/ß 2 e. α 3 + ß 3 (Ans:-1, 4/5 ,-6,
y+7 3y-2 --- = 1 + ---- 3 5
37x7= multiply answer it.
1
Write down a game each to teach children i) multiplication, ii) what a circle is, iii) estimation skills. Also say what you expect the child to know before you try to t
The Definition of the Limit In this section we will look at the precise, mathematical definition of three types of limits we'll be looking at the precise definition of limits
Jocelyn has 6 birds, Their mean age is 10. The mode of their ages is 8. What might their ages be? Show your work.
log6 X + log6 (x-5) = 1
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