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f(x) =\frac{1}{2}x^2-2x. Natural Language; Math Input; Extended Keyboard Examples Upload Random. Compute answers using Wolfram's breakthrough technology & knowledgebase, relied on by millions of students & professionals. For math, science, nutrition, history, geography, engineering, mathematics, linguistics, sports, finance, music…

The inverse function of F (x) = − 2 1 (x + 3) is F − 1 (x) = − 2 x − 3. This means that applying F and then F − 1 will return you to your original input. Inverse functions fundamentally reverse the operations performed by the original function.

What I did so far: \\begin{align*} \\frac{x-1}{x+2}&=(\\frac{x-1}{2})\\frac{1}{1-(-\\frac{x}{2})} \\\\ &=(\\frac{x-1}{2})\\sum_{n=1}^\\infty (-\\frac{x}{2})^n ...

I'd like to show that the MacLaurin series of the function in question is $ \sum_{n=0}^{\infty}\binom{-1/2}{n} x^{2n}$, where $ \binom{-1/2}{n} $ is the generalized ...

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Even though $𝑓(2)$ is undefined at $ℎ=0$, as long as $𝑓(2)$ does not actually depend on $ℎ$, treating it as a constant and focusing on how $𝑓(2)$ / $ℎ$ behaves as $ℎ$ approaches 0 is valid for finding the limit.

domain of f(x) = x/(x^2-1) Compute the range of a function: range of e^(-x^2) More examples. Polynomials . Solve, plot and find alternate forms of polynomial expressions in one or more variables. Compute properties of a polynomial in several variables: x^3 + x^2 y + x y^2 + y^3. Factor a polynomial:

Then the number of values of x in [0,1] for which \(f^{[2005]}(x) = \frac {1}{2}\) can be expressed in the form \(p^a\), where p is a prime and a is a positive integer. Find p+a. Find p+a. Guest Jan 20, 2019

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What is actually true is the trivial observation that (by the mean value theorem) $$ \frac{1-f^2(x)}{1-x^2}=f'(c) \frac{1+f(x)}{1+x} \le f'(x)\frac{1+f(x)}{1+x} , $$ and it seems this is as far as we can go in general.

You are right: The function defined by $$ f(x) = \frac{1}{x} $$ is a rational function. Some might call this the Harmonic function, but I don't think that this is a good idea because there is a (probably) more common notion of a Harmonic function.. The graph of the function is a Hyperbola.. Now, we do also have something called a Harmonic series.

Find the derivative of $ f(x) = \frac{ln x}{x} $ at the point $ x = e^2 $. Related calculators. 1: Limit calculator. 2: Integral calculator. Find more worked-out examples in our database of solved problems. Examples of valid and invalid expressions. Function to differentiate ...

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