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Define an ordered rooted tree. Cite any two applications of the tree structure, also illustrate using an example each the purpose of the usage.
Ans: A tree is a graph like that it is connected, it has no loop or circuit of any length and number of edges in it is one less as compared to the number of vertices.
If the downward slop of an arc is taken as the direction of the arc after that the above graph can be considered as a directed graph. In degree of node + is zero and of all other nodes is one. There are nodes such as 3, 4, 5, 2 and 5 without degree zero and all other nodes comprise out degree > 0. A node with in degree zero in a tree is known as root of the tree. Each tree has one and just only one root and that is why a directed tree is as well known as a rooted tree. The position of each labeled node is fixed, any change in the position of node will modify the meaning of the expression denoted by the tree. Such kind of tree is called ordered tree.
A tree structure is utilized in evaluation of an arithmetic expression (parsing technique) The other common application is search tree. The tree presented is an instance of expression tree. An instance of binary search tree is shown below.
Let u = sin(x). Then du = cos(x) dx. So you can now antidifferentiate e^u du. This is e^u + C = e^sin(x) + C. Then substitute your range 0 to pi. e^sin (pi)-e^sin(0) =0-0 =0
1. Consider the following differential equation with initial conditions: t 2 x'' + 5 t x' + 3 x = 0, x(1) = 3, x'(1) = -13. Assume there is a solution of the form: x (t) = t
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Water in a canal 30 dm wide and 12 dm deep is flowing with a velocity of 10 km/h. How much area will it irrigate in 30 minutes if 8 cm of standing water is required for irrigation?
Assume that the amount of money in a bank account after t years is specified by, Find out the minimum & maximum amount of money in the account throughout the first 10 years
Solve the subsequent IVP. cos(x) y' + sin(x) y = 2 cos 3 (x) sin(x) - 1 y(p/4) = 3√2, 0 Solution : Rewrite the differential equation to determine the coefficient of t
Consider the following interpolation problem: Find a quadratic polynomial p(x) such that p(x0) = y0 p’(x1) = y’1 , p(x2) = y2 where x0 is different from x2 and y0, y’1 , y2 a
Example of Log Rules: Y = ½ gt 2 where g = 32 Solution: y = 16 t 2 Find y for t = 10 using logs. log y = log 10 (16 t 2 ) log 10 y = log 10 16 + log 10
Recognizes the absolute extrema & relative extrema for the following function. f ( x ) = x 2 on [-1, 2] Solution: As this function is simpl
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