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Derivative and Differentiation
The process of acquiring the derivative of a function or slope or gradient is referred to as differentiation or derivation. The derivative is denoted by (dy)/(dx) or f (x) and is provided by dividing the change in y variable by the change in x variable.
The derivative or slope or gradient of a line AB connecting points (x,y) and (x+dx, y + dy) is specified by
(Δy)/(Δx) = (change in y)/(change in x)
= (((y + (dy)) - y)/ (((x + (dx)) - x)
Whereas dy is a small change in y and dx is a small change in x variables.
2x+2y=10 and 3y+4x=9
Monotonic, Upper bound and lower bound Given any sequence {a n } we have the following terminology: 1. We call or denote the sequence increasing if a n n+1 for every n.
1. Consider a source with 4 symbols {a,b,c,d}. The probability of the 4 symbols are P(a)=0.4, p(b) = 0.1, p(c)=0.2, p(d)= 0.3. a. Design a Huffman codebook for these symbols.
Calculate the mean, variance & standard deviation of the number of heads in a simultaneous toss of three coins. SOLUTION: Let X denotes the number of heads in a simu
Decision making under uncertainty Various methods are used to make decision in circumstances whereas only the pay offs are identified and the likelihood of every state of natur
-5+-6=
Use L''hopital''s rule since lim X-->0 1-cos(x)/1-cos(4x) is in the indeterminate form 0/0 when we apply the limt so by l''hoptital''s rule differentiate the numerator and den
1 . The probability that a couple will have a child with black hair is 0.6. If this couple has 7 children what is (a) the probability that exactly 3 of these children have bl
1. Write down the canonical equations of the line passing through the point A(2,3, 4) and being parallel to the vector q ={5,0,-1}.
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