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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
Sketch several trajectories for the system, x 1 ' = x 1 + 2x 2 x 2 ' = 3x 1 + 2x 2
The scale of a map is 0.5 in 25mi the actual distance between two cities is 725mi write a proportion that represents the relationship how far apart will the cities be on the map
Given that f(x,y) = 3xy - x 2 y - xy 2 . Fi nd all the points on the surface z = f(x, y)where local maxima, local minima, or saddles occur
if Mr.Ibias oredered a rectangular pizza and he wants 2/3 of the pizza to be pepperoni and 1/2 of the pizza with pineapple draw and label the pizza with toppings explain your think
A bag contains 5 red balls and some blue balls. If the probability of drawing a blue ball is double that of a red ball , determine the number of blue balls in the bag.
Arc Length - Applications of integrals In this part we are going to look at determining the arc length of a function. As it's sufficiently easy to derive the formulas that we'
Reasons why we start division : The reason we start division by considering the digit in the leftmost place is efficiency and ease . For instance, suppose we divide 417 by 3, we
Slope of Tangent Line : It is the next major interpretation of the derivative. The slope of the tangent line to f ( x ) at x = a is f ′ ( a ) . Then the tangent line is given by,
Question 1: What is the minimum number of students each of whom comes from one of the 50 different states, enrolled in a university to guarantee that there are at least 100 who
Example 1 Add 4x 4 + 3x 3 - x 2 + x + 6 and -7x 4 - 3x 3 + 8x 2 + 8x - 4 We write them one below the other as shown below.
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