Asked by Jamie
Approximate the following value using derivatives (without a calculator)
(1.1)^4 - (1.1)^2
I only know how to do linear approximation when using square roots. How do I do this type of problem?
(1.1)^4 - (1.1)^2
I only know how to do linear approximation when using square roots. How do I do this type of problem?
Answers
Answered by
Murkle
The final answer would be 1.21
First subtract:
(1.1^4) - (1.1^2) = 1.1^2
then solve:
(1.1)^2 = 1.21
How it works:
If you have x^4 - x^2 and the value of x is the same, just subtract the exponents. x^4 - x^2 = x^2
Google search exponent and go to mathisfun for more info and practice.
In this case 1.1^4 is just 1.1 * 1.1 * 1.1 * 1.1
so you can subtract 1.1^2 which is 1.1 * 1.1 from that, and get 1.1 * 1.1 .
1.1 * 1.1 = 1.21
Good Luck!
First subtract:
(1.1^4) - (1.1^2) = 1.1^2
then solve:
(1.1)^2 = 1.21
How it works:
If you have x^4 - x^2 and the value of x is the same, just subtract the exponents. x^4 - x^2 = x^2
Google search exponent and go to mathisfun for more info and practice.
In this case 1.1^4 is just 1.1 * 1.1 * 1.1 * 1.1
so you can subtract 1.1^2 which is 1.1 * 1.1 from that, and get 1.1 * 1.1 .
1.1 * 1.1 = 1.21
Good Luck!
Answered by
Murkle
P.S. Can't edit here..
The exponent of a number says how many times to use the number in a multiplication of itself.
The exponent of a number says how many times to use the number in a multiplication of itself.
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