I used √x+3 to approximate √3.98 and √4.05. Therefore, I have to plug in the values of x that will make √x+3 equal to √3.98 and √4.05. Since 0.98+3=3.98 and 1.05+3=4.05, I use 0.98 and 1.05 for x.
Yes, you could carefully graph the functions by hand instead of using a calculator, use a table of values, or solve the equation 7/4+x/4=sqrt(x+3)+0.5 algebraically, but these are all fairly cumbersome methods. The question is designed for use with a calculator.
00:00 Linear Approximation
01:57 Example 1
06:58 Example 2
13:25 Independent Variables
15:25 Example 3
19:04 Example 4
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How did 3.98 become .98 and how did 4.05 become 1.05 when you plugged them in? So confused
I used √x+3 to approximate √3.98 and √4.05. Therefore, I have to plug in the values of x that will make √x+3 equal to √3.98 and √4.05. Since 0.98+3=3.98 and 1.05+3=4.05, I use 0.98 and 1.05 for x.
@@asherroberts Wow! That makes a lot of sense; thank you!
is it possible to do what you did on the calculator without the calculator?
Yes, you could carefully graph the functions by hand instead of using a calculator, use a table of values, or solve the equation 7/4+x/4=sqrt(x+3)+0.5 algebraically, but these are all fairly cumbersome methods. The question is designed for use with a calculator.