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Number and Square Root Rewritten
- Thread starter Jason76
- Start date
They (all three) are all equivalent. If someone had meant the square root of 2x (which is equivalent to 2x raised to the 1/2 exponent, then it would be typed as \(\displaystyle \sqrt{2x} \ \ or\ \ (2x)^{1/2}, \ \ \)for instance. It's the Order of Operations in effect.Is \(\displaystyle 2\sqrt{x} = 2x^{1/2}\) or \(\displaystyle 2(x^{1/2})\) ? If you saw this in a problem, the how to deal with it? Do we deal with the number and "x to the 1/2 power" separately or as the same thing?
So is this off to a right start?
\(\displaystyle 2\sqrt{x}\dfrac{dy}{dx} = \sqrt{(1 - y^2)}\)
Rewritten using 1/2 power.
\(\displaystyle 2(x)^{1/2}\dfrac{dy}{dx} = (1 - y^{2})^{1/2}\)
\(\displaystyle (dx) 2(x)^{1/2}\dfrac{dy}{dx} = (1 - y^{2})^{1/2}(dx)\)
\(\displaystyle 2(x)^{1/2} dy= (1 - y^{2})^{1/2}dx\)
\(\displaystyle (\dfrac{1}{x^{1/2}})2(x)^{1/2}dy= (1 - y^{2})^{1/2}(\dfrac{1}{x^{1/2}})dx\)
So is this off to a right start?
Yes. That looks good so far.