Hi,
If all x,a,b and c are all natural numbers, is this true?
x^{a^b} = (x^{a^{b-1}})^a
Proof
if c = a^{b-1}
ca = (a^{b-1})a = a^b
and (x^c)^a = x^{ca} = x^{a^b}
Could I please have some feedback on this,
Thanks
\sqrt[3]{2}\inF with a=0 and b=1
So there must be c such that c*\sqrt[3]{2}=1
c=1/\sqrt[3]{2}\notinQ
Since \sqrt[3]{2}\inF, F must not be a field because it has no inverse under multiplication.
Is this sound?
Homework Statement
Let F = {a + b\sqrt[3]{2}:a,b\inQ}.
Using the fact that \sqrt[3]{2} is irrational, show that F is not a field.
[Hint: What is the inverse of \sqrt[3]{2} under multiplication?]
Homework Equations
For a field,
For all c \in F, there exists c-1 \in F s.t. c*c-1 =1...
Thanks Sammy,
Now I see that I made a mistake at the very beginning.
I wanted to integrate \int \frac{e^{x^2}(x^2-1)+1}{x^4} xdx in which case I think the integral is correct, and still unsure where the 5 comes from?
\int \frac{e^{x^2}(x^2-1)}{x^4} xdx using the substitution suggested I got, \int \frac{e^{u}(u-1)}{2u^2} du= \frac{e^{u}-1}{2u} .
Substituting back to x, \frac{e^{x^2}-1}{2x^2} . The limits on the integration were from 0 to 2.
\frac{e^{4}-1}{8} - 0 = 6.6997...
However, when I do this on...
Homework Statement
The temperature of a point on a unit sphere, centered at the origin, is given by
T(x,y,y)=xy+yz
Homework Equations
I know that the equation of a unit sphere is x^2+y^2+x^2=1, which will be the constraint.
The Attempt at a Solution
The partial derivatives of T are...
Thanks!
I know the answer is \frac{exp(x)}{2x}, becuase I can confirm it using the quotient rule for differentiation, but could someone please explain how to show the integration process?
Homework Statement
I need to find the integral of \frac{exp(x^{2})(x^{2}-1)}{x^{3}}
Homework Equations
Wolfram returns this answer
\frac{exp(x^{2})}{2x}
The Attempt at a Solution
I orginally had the integral in the form of:
\frac{exp(x^{2})(x^{2})}{x^{3}}-\frac{exp(x^{2})}{x^{3}}...
I am trying to find the level curves for the function g(x,y)= k = xy/(x^2+y^2).
I get, x^2+y^2-xy/k=0.
I know this is an ellipse, but I do not know how to factor, and find values of k for which the level curves exist.