If y varies directly as x and y is 12 when x is 1.2, what is the constant of variation for this relation?.
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At each step, you determine the quotient term by dividing the highest-degree term of the dividend by the highest degree term of the divisor. When you can't do that anymore, you're done and the remaining dividend is the remainder.
Here, the highest-degree dividend term is x^2 and the highest-degree divisor term is x. Their ratio, x^2/x = x, is the first quotient term. In the usual manner of long division, you subtract the product of this quotient term and the divisor to get the new dividend.
For this problem, the quotient is (x -5) and the remainder is 5. You can write the result as
(x² -10x +30)/(x -5) = (x -5) +5/(x -5)
Here, the highest-degree dividend term is x^2 and the highest-degree divisor term is x. Their ratio, x^2/x = x, is the first quotient term. In the usual manner of long division, you subtract the product of this quotient term and the divisor to get the new dividend.
For this problem, the quotient is (x -5) and the remainder is 5. You can write the result as
(x² -10x +30)/(x -5) = (x -5) +5/(x -5)
The function is a continuous function at 2 if the LHL and RHL will be the same as the limit of the function.
<h3>What is continuity of a function?</h3>It is defined as the property of a function in which the function varies continuous, and we plot the graph of a function it doesn't break.
We have a function:
If f(x) is a continuous, then it will follow:
f(2) = 2² - 2 = 4 - 2 = 2
Left-hand limit at 2 = right-hand limit at 2 = 2
Limit at 2 of a function = 2
Using limit, we can check the whether the function is differentiable or not.
Thus, the function is a continuous function at 2 if the LHL and RHL will be the same as the limit of the function.
Learn more about the continuous function here:
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