-1
votes
1answer
41 views

How to estimate the upper bound of y in this situation? [closed]

How to estimate the upper bound of y in this situation? Given 1. a function $y=f(x_1,x_2,x_3,x_4,x_5)$ with 5 parameters ($y=f(...)$ can be any function). 2. for each $x_i$ there are $k_i$ possible ...
3
votes
4answers
186 views

Using $(1+x)^k \approx 1+kx$ to approximate?

Use the approximation $(1+x)^k \approx 1+kx$ to estimate $(1.0003)^{26}$ and $\sqrt[4]{1.006}$. I know how to solve this step-by-step, but I don't understand what I'm doing exactly: why does ...
0
votes
2answers
184 views

Estimate a value knowing the values of: the function, the derivative and the second derivative in 0

Please suppose you have an unknown function r(x). This function r(x) is defined in the range: [-5; 5] You know that: r(0) = 1; r'(0) = -1; r"(0) = 1. Please estimate the value of r(x) in the ...
2
votes
1answer
20 views

Estimation for large $k$.

I have a function $f(k)$ defined on the set of natural numbers and I managed to show that $f(k)>n-\binom n k(1-n^{-2/3})^{k(k-1)/2}$ for all integers $n\ge k$. I am hoping to get a further ...
0
votes
1answer
47 views

Estimating the derivative of a $C_0^\infty$ function.

Let $w \in C_0^\infty(\mathbb{R},\mathbb{R}^+)$ be a function with $\int_\mathbb{R} w(x) = 1$. What can we say about the first derivative, or what can we say about $\int_\mathbb{R} |\partial_xw|$ ? ...
0
votes
1answer
80 views

Is the hypergeometric function $F(5/4,3/4; 2, z)$ bounded on $(0,1]$

Consider the classical hypergeometric function $F(5/4,3/4; 2, z)$ for $z\in (0,1]$. Is this bounded by some real number (independent of $z$)? I'm aware of Euler's formula: $$F(5/4,3/4; 2, z) = ...
4
votes
2answers
229 views

Bound for the Legendre function of the second kind of degree $1/2$

Let $Q_{1/2}(u)$ be the Legendre function of the second kind of degree $1/2$. One can show that $Q_{1/2}(u) = O(u^{-3/2})$ as $u\to \infty$; see Equation 21 in Section 3.9.2 of Higher transcendental ...