Recent content by deancodemo

Thankyou everyone for your help. :)

You're right, I haven't given a definition of sin(x). Without knowing what exactly sin(x) is, the only information that can be used to find its derivative is the limit of sin(x)/x. My motivation for starting this thread was actually finding a purely algebraic (ie. non geometric) method of...

What other means? I am only aware of the difference quotient (or whatever its called) to find the derivative of a function.

Consider the following derivation of sin'(x): \frac{d}{dx}\sin x = \lim_{h \to 0} \frac{\sin(x + h) - \sin x}{h} = \lim_{h \to 0} \frac{\sin x \cos h + \cos x \sin h - \sin x}{h} = \lim_{h \to 0} \frac{\sin x (\cos h - 1) + \cos x \sin h}{h} = \lim_{h \to 0} \frac{\sin x (\cos h - 1)}{h} +...

Yes, this is true. Isn't Euler's formula derived using the Taylor expansion of sinx (which relies on the derivative of sinx)?

I wish to prove \lim_{x \to 0} \frac{\sin x}{x} = 1 using L'Hôpital's rule. The problem with this is, even though the result after applying the rule is 1 (the correct answer), the limit itself was assumed to be correct in order to calculate the derivative of sinx. This constitutes circular...

Here is an easier way. Given 2-i is one root, then another root is 2+i (since coefficients are real, complex roots occur in conjuagate pairs). Now, call the last root x. Sum of roots = (2-i) + (2+i) + x = -b / a = 3. Upon simplifying, x = -1. Done!

Homework Statement If a, b, c > 0, prove \frac{a}{b} + \frac{b}{c} + \frac{c}{a} \ge 3 Homework Equations The Attempt at a Solution I'm not so sure how to do this. Usually I would try to prove that \frac{a}{b} + \frac{b}{c} + \frac{c}{a} - 3 \ge 0 but this gets me nowhere...

Ok, here's my working: (a + b)^2 = 3 - 2 \sqrt 2 a^2 + b^2 + 2ab = 3 - 2 \sqrt 2 a^2 + b^2 = 3 \quad (1) <--- (is this because a^2 + b^2 is a rational?) 2ab = -2 \sqrt 2 ab = - \sqrt 2 \quad (2) (from 2): a = \frac{-\sqrt 2}{b} \quad (3) (from 1): a^2 + b^2 = 3 (\frac{-\sqrt 2}{b})^2...

Homework Statement Find the square root of 3 - 2\sqrt 2. Homework Equations The Attempt at a Solution I don't really know how to do this quickly. Could this be done by solving x^2 = 3 - 2\sqrt 2? Or should I solve (a + b)^2 = 3 - 2\sqrt 2? By the way, the answer is 1 - \sqrt 2.

From http://en.wikipedia.org/wiki/Differential_(infinitesimal)" : Differentials are also used in the notation for integrals because an integral can be regarded as an infinite sum of infinitesimally small quantities: the area under a graph is obtained by subdividing the graph into...

I found a good wiki page about this topic http://en.wikipedia.org/wiki/Differential_(infinitesimal)" . Also, \delta x is small, but dx is infinitely small.

Yes, yes. Another thing people tend to write is \lim_{\delta x \to 0} \frac{\delta y}{\delta x} = \frac{dy}{dx}. I guess this means that as \delta x becomes very small, the quotient \frac{\delta y}{\delta x} becomes exact. ie the derivative \frac{dy}{dx}.

This isn't really a homework question, but it has been bugging me for ages. In \int f(x) \, dx what exactly does the 'dx' represent? Is it a differential? What is a differential? I only use the 'dx' part to identify the variable that the function is being integrated with respect to... or...

Homework Statement Two particles of masses 2kg and 1kg are attached to a light string at distances 0.5m and 1m respectively from one fixed end. Given that the string rotates in a horizontal plane at 5 revolutions/second, find the tensions in both portions of the string. Homework Equations...