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Note 3:
d y and dy are not usually the same and dy is the approximate value of d y..
d y and dy are not usually the same and dy is the approximate value of d y..Example:
Find the approximate value of fourth root of 82 upto 3 decimal place..
Curve Sketching
The graph of a given function gives a visual presentation of the behaviour of the function involving a study of symmetry, rise and fall, region of existence, passage through specific points etc. The following points are helpful to trace the curv..
Example:
Sketch the curve y = - sin 2x ...
Passage through origin
Put x = 0, y = -sin2x = 0. This implies (0, 0) is a point on the curve or the curve passes through the origi..
Determination of Few Point
with this information, we sketch the graph as show ...
with this information, we sketch the graph as show ...Example:
Define The graph of the function is as follows: f(x) is increasing, because Since 2 - 1 < 3 - 1 (ii) f is said to strictly increasing in the interval I if For example, Let x 1 < x 2 f(x) is strictly increasing function. (iii) f(x) is said to be decreasing function if f..
Define The graph of the function is as follows: f(x) is increasing, because Since 2 - 1 < 3 - 1 (ii) f is said to strictly increasing in the interval I if For example, Let x 1 < x 2 f(x) is strictly increasing function. (iii) f(x) is said to be decreasing function if f..Example:
Find the intervals on which the function (a) increasing (b) decreasing Differentiating the function, we have The critical values in ascending order are -1, 1. We divide the Real numbers into the intervals = - ve Since f '(x) < 0, the function is decreasing in the interval ..
Find the intervals on which the function (a) increasing (b) decreasing Differentiating the function, we have The critical values in ascending order are -1, 1. We divide the Real numbers into the intervals = - ve Since f '(x) < 0, the function is decreasing in the interval ..Geometrical meaning
Let A (a,f (a)) and B (b,f (b)) be two points on f (x), then ..
Let A (a,f (a)) and B (b,f (b)) be two points on f (x), then .. Result
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