We can write this condition as: limx→b−g(x)=limx→b+g(x) Answer and Explanation:1 All differentiable functions are continuous, but it is not necessary that all continuous functions are differentiable. Suppose a functionf(x)is... ...
a) If a function is differentiable at a point, that means its derivative exists at that point as well. Using mathematical notation, we can state that...Become a member and unlock all Study Answers Start today. Try it now Create an ...
An extremum (or sometimes a point of inflection) will exist where the derivative is zero, assuming the function is differentiable. That expression can only ever be zero when the numerator is zero, or as a limit if the denominator approaches +/- inf. But ...
The condition number is the ratio of the change in output for a change in input in the ‘worst-case’—that is to say, at the point when the change in output is largest per given change in input. If a function is differentiable and in just one variable, the condition number can be ...
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aJt (x0, x ) is a concave homogeneous differentiable function Jt (x0, x)是一个凹面同类的可微函数[translate] aI hate you!your is bendan and shagua 我恨您! 您是bendan和shagua[translate] aIn addition,I have another question to confirm with you 另外,我有另一个问题证实与您[translate] ...
Finding the derivative of other powers of e can than be done by using the chain rule. For example e2x^2is a function of the form f(g(x)) where f(x) = exand g(x) = 2x2. The derivative following the chain rule then becomes 4x e2x^2. ...
Absolutely Integrable Function Defined on an Interval Many times, you’ll deal with functions that aren’t absolutely integrable on their entiredomain. However, the condition can be defined in terms ofintervals. For example, take some functionf, defined on theopen interval(a,b). If the function...
Theorem 1.What is the proof? If M(x, y) and N(x, y) are both homogeneous and of the same degree, the function \frac{M(x, y)}{N(x, y)} is homogeneous of degree Zero. Theorem 2.If f(x, y) is homogeneous How can it be proved that the space \mathbb{P} of all polynomial...
Show that the function f(x) = | x - 2 | is not differentiable at 2. Show that the function is differentiable: f(x, y) = xy - 5y^2 Let u be a differentiable function of x. Use the fact that |u| = \sqrt{u^2} to prove that \frac{d}{dx}[|u|]=u'\frac...