Unitary Method
The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products.
Speed, Time, and Distance
Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 miles away.
Profit and Loss
The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.
Units and Measurements
Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experiments to set up the devices.
![< Chapter 2.5, Problen
Theorem used: The Intermediate value Theorem
Suppose that if fis continuous on the closed interval [a, b] and let
number between f (a) and f (b), where f (a) + f (b). Then,
there exists a number cin (a, b) such that f (c) = N.
be
any
Proof:
Consider the function f (x) = x² + 10 sin x.
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Here, f (x) is a combination of polynomial and trigonometric
function. Both are continuous everywhere. Therefore, f (x) also
continuous on R.
Without loss of generality, take the subinterval [31, 32] C R.
Take a = 31, b = 32 andN = 1000.
Substitute 31 for x in f (x),
f (31) = (31) + 10 sin (31)
961 + 10 (-0.40404)
= 961 – 4.0404
2 957
This implies that, f (31) = 957 < 1000.
Substitute 32 for x in f (x),
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Short Answer: Yes the values 31 and 32 are specific to this problem only.
Explanation: We are given the function , we need to show that there exist a number c such that f(c)=1000.
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