How to prove a manifold is differentiable? How to find out the boundary conditions? How to check if a set is a basis in \mathbb{P}_3? How to show a lower bound does not exist for a function stack? f(x) = e^{-x^2} is concave down on ___ . Verify that...
How to prove a function is infinitely differentiable? How to prove there is no lower bound for a continuously differentiable function? Let c greater than 0 and f : [-c, c] approacches R a continuous function, differentiable on (-c, c), such that f' (x) less than or equal to 1 ...
例如a)不连续的，如y=u(t)表示阶跃函数就是不可微的 b）连续但是两侧极限不等，如|x|在x=0处
Alldifferentiable functions(i.e., all functions with a derivative at every point in its domain) are continuous, but not allcontinuous functionsare differentiable. The only way for the derivative to exist everywhere is if the function also exists on its domain. Just because a function is continuo...
implementation of number systems and conversions between them. We see that x is irrational iff x isn't in the range of the embedding function, i.e, x is a real number that doesn't correspond to any rational number. We check that it agrees with our intuition what "being irrational" ...
forhto 0, these points will lie infinitesimally close together; therefore, it is the slope of the function in the pointx.Important to note is that this limit does not necessarily exist. If it does, the function is differentiable; if it does not, then the function is not differentiable. ...
aTaylor ' s Theorem, which will be introduced in this section, is a basic theorem to show how to approximate a given differentiable function by means of polynomials which has important applications in theoretical research and approximate calculations. 泰勒‘s定理,在这个部分将被介绍,是显示如何的一...
Let g(x) and h(y) be differentiable functions, and let f(x, y) = h(y)i+ g(x)j. Can f have a potential F(x, y)? If so, find it. You may assume that F would be smooth. (Hint: Consider the mixed partial derivatives of F.) How to answer this question? W...
Related to this Question How to prove that a function is differentiable everywhere? Suppose that y = f(x) is a differentiable function. Prove: \frac{df}{dx} \cdot \frac{x}{f(x)} = \frac{d \ln f(x)}{d \ln x} How to show if function is differentiable?
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