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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".
OTHER WAYS TO AID LEARNING : Here we shall pay particular attention to the need for repetition, learning from other children, and utilising errors for learning.
1. In 1900, a certain country's population was 77,977,459 and it's area was 2,821,924 square miles, In 2000, the country's population was 283,575,229 and its area was 3,551,003 sq
How could 2+2 will be Equal to 5
Q. Determine the probability of tossing a head? Let B represent the event of tossing a heads with the nickel in example 2. Find P(B). Solution: S = {(H, H), (H, T), (T, H
samuel left mauritius at 22:30 on saturday and travelled to london (GMT) for 14h30min he had a stopover for 4 h in london and he continued to travel to toronto for another 6h20min
Harold used a 3% iodine solution and a 20% iodine solution to make a 95- ounce solution in which was 19% iodine. How many ounces of the 3% iodine solution did he use? Let x = t
project assignment of page no.19 question no.2
ABCD is a rhombus. the sides of the rhombus are 8cm long .one of its diagonals is 12cm .find the angels of the rhombus
cos(x)y''+sin(x)y=2cos^3(x)sin(x)-1
A circle touches the sides of a quadrilateral ABCD at P, Q, R and S respectively. Show that the angles subtended at the centre by a pair of opposite sides are supplementary.
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