A Word problem on Surd with Algebraic Expression

Surd with an algebraic expression can be simplified as shown in the example below.Finding cube root and square root are basic of surd.

Topic : Solving a surd

In the problem shown below explains how to find square root of any algebraic expressions. For more problems on surd please see indice math.

Question : Suppose that N= √x + 4 models the number of cases of an infection, inmillions, of a disease x years from now.
(a) Approximately how many cases of the infection will there be 16years from now?
(b) In approximately how many years will there be 6 million cases?

(a) Solution :

Given x = 16.
So, number of cases of infection will be found as:
N = √x + 4
= √16 + 4
= 4 + 4
= 8

So, There will be approximately 8 cases of the infection 16 years from
now.

(b) Solution :

Given N = 6
So, number of cases of infection will be found as:
N = √x + 4
=> 6 = √x + 4
=> 6 – 4 = √x
=> 2 = √x
=> √x = 2

Squaring both sides we get
x = 2²
=> x = 4

So,In 4 years, there will be 6 million cases.

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Question on Differentiation using First Principle

Here is a problem on Differentiation using First Principle and resultant applying limits.


Topic : First Principle of Differentiation


A simple problem on first principle of differentiation.


Question: Differentiate by first principle.

-12x² -11x - 1 and given function [f(x+h)- f(h)]/h

Solution :





















Above Differentiation using first principle will be an best and simple example to solve similar kind of problems, if you have any queries do write to calculus help.