Modulus (Absolute value) of an integer
Absolute value (or modulus) of an integer is the numerical value regardless of its sign. Absolute value of an integer x is written as bars on either side of the expression i. e |x| and is defined as |X| = X if x ≥ 0 = -X if x < 0 Example: Absolute value of –5 is written as |-5| and its value is 5. Similarly, Absolute value of 5 is written as |5| and its value is 5. Properties of absolute value function
If we plot |x| against x then we ‘ll get a graph as shown below.
1. The real absolute value function is continuous everywhere. 2. It is differentiable everywhere except for x = 0. 3. Absolute value function is monotonically decreasing on the interval (-∞, 0] and monotonically increasing on the interval [0, ∞). 4. Any real number and its negative have the same absolute value, so absolute value function is an even function. 5. |X| = |-X|
6. |XY| = |X| |Y|
7. |X/Y| = |X| / |Y|
8. If |X| ≤ K => -K ≤ X ≤ K 9. If |X - Y| ≤ K => -K ≤ (X – Y) ≤ K => Y-K ≤ X ≤ Y + K Ex1 : Find the value of (| x- y| + |y –x|) where 2x – 7 = x + y. 2x – 7 = x + y
=>x – y = 7 and | x- y| = 7
y – x = 7 and |y –x| = 7 So the answer is 14.
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Hi fnds
I lost the track of the discussion forums that are just started on the topics of quant
Let me know the topics that are discussed and the current topics being discussed
I'll plan myself accordingly
Thank you
Gopi
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We are yet to start things in full flow and it’s just the first topic. . . I guess it ‘ll take some time to have some guys on board . . so don’t worry, you have not missed much. .
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