112. True, or false? Give reasons for your answers.
a. 1...

Question

112. True, or false? Give reasons for your answers.

a. 1/x⁴ = O(1/x² + 1/x⁴)

Accepted Answer

Determine whether the statement is true or false. 1 divided by X 6 equals O of 1 divided by X4 plus 1 divided by X 6. We have answers true or false. Now, a big O notation, which is the O in front of our equation. Is used to describe an upper bound on the growth rate of a function. We can say F of X equals O G X. This means that there exists positive constant C and X0 such that for all X greater than X, we have F X divided by G of X. As less than some constant c. Or we can then say absolute value of f x. is less than equals a c multiplied by g of x and the absolute value. Vicious means that F of X does not grow faster than G of X multiplied by some constant c beyond some point x 0. Now let's apply it to our functions. We want to see if 1 divided by x 6 is bounded above by a constant multiplied by g of x. So, we can say F X divided by G of X. Equals 1 divided by x 6, all divided by 1 divided by x 4, plus 1 divided by x 6. We can then simplify these ratios, 1 divided by X 6 multiplied by X4 x 6, all divided by x 6 + x 4. Now from here we can simplify. This gives us 1 divided by X2 + 1. And we will set this less than equals to 1. We can then say that F of X. As lesser equals to 1 multiplied by g of x. For all X greater than 0. This then confirms that F of X equals o g x. And we would set our constant equals to one, so we can say that our statement is true. That means the answer to our problem is answer A. OK, I hope to help you solve the problem. Thank you for watching. Goodbye.

112. True, or false? Give reasons for your answers.a. 1/x⁴ = O(1/x² + 1/x⁴)

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112. True, or false? Give reasons for your answers.
a. 1/x⁴ = O(1/x² + 1/x⁴)