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We have seen that if y is a function of x, then for each given value of x, we can determine uniquely the value of y as per the functional relationship. For some functions, it is possible to express x in terms of y so that, given the value of y, the value of x can be uniquely determined. The function that expresses the variable x in terms of the variable y is called the inverse function and is denoted by x = f-1 (y).
Example
y = f(x) = 5x + 3
Solving x in terms of y,
x
Theorem a → • b → = ||a → || ||b → || cos• Proof Let us give a modified version of the diagram above. The three vectors above make the triangle AOB and note tha
Without solving, find out the Wronskian of two solutions to the subsequent differential equation. t 4 y'' - 2t 3 y' - t 8 y = 0 Solution : First thing that we want to d
find the value of x for which the distance between the points p(4,-5) and q(12,x) is 10 units
Example: Joanne is given a four-question multiple-choice quiz. She hasnt studied the material to be quizzed, so she decides to answer the questions by randomly guessing the answe
Q. Graphs of Sin x and Cos x ? Ans. The sine and cosine functions are related to the path that an object might take around a circle. Suppose a dolphin was swimming over
solve and graph the solution set 7x-4 > 5x + 0
Calculus with Matrices There actually isn't a whole lot to it other than to just ensure that we can deal along with calculus with matrices. Firstly, to this point we've onl
explanation
real life applications of lengrange''s mean value theorem
If you have 60% alcohol and wish to dilute with water to make 12 liters 40% alcohol, How many liters of water should you add?
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