Learn about differentiability. Understand how to tell if a function is differentiable and when it isn't and see a comparison of differentiable vs. continuous. Related to this Question How to prove figure eight is not a manifold? How to give a closed manifold a boundary?
Learn about differentiability. Understand how to tell if a function is differentiable and when it isn't and see a comparison of differentiable vs. continuous. Related to this Question How to prove that a function is differentiable everywhere?
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
If f '(x) = \frac{(2x + 1)^2}{ x} \enspace and \enspace f(2) = 0 , what is f(1) ? Express \ln 0.375 in terms of \ln 2 \enspace or \enspace \ln 3 Suppose that f \enspace and \enspace g are functions which are differenti...
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...
The absolute value parent function. The absolute value parent function is written as: f(x) = │x│ where: f(x) = x if x > 0 0 if x = 0 -x if x < 0 As the definition has three pieces, this is also a type ofpiecewise function.It’s only true that the absolute value functio...
If I have two points, say, P1, P2 connected by a spring, I need their Euclidian distance to know the force of the spring. How can one get this distance without sqrt(..)? This is the only example I could think of as well. In 1D Hooke's law is linear but in more than 2D Hooke...
This is to say that any point at which the derivative of a function is zero or nonexistent is called a critical point. Recall that the derivative of a function informs about the slope of the function at any point within the domain. If the derivative of the function is zero at a point...
Stationary point of a function is a point where the derivative of a function is equal to zero and can be a minimum, maximum, or a point of inflection
g(b) is the function value at point x = b. To confirm if the limit exists, we need to check the one sided limits of the function. The one sided limits are left hand limit and the right hand limits. We can write this condition as: {eq}\displaystyle { \lim_{x \to b^-} g(...