Brain Teaser - Area enclosed by a parabola and a line
09-16-2015, 05:12 AM
Post: #24
 Thomas Klemm Senior Member Posts: 1,610 Joined: Dec 2013
RE: Brain Teaser - Area enclosed by a parabola and a line
(09-16-2015 02:06 AM)Gerson W. Barbosa Wrote:  The equation of the normal line shouldn't be difficult to derive, but it's ready for use on page 70:

$y-y_{1}=-\frac{1}{\frac{dx}{dy}}(x-x_{1})$

There's a typo: $$dx$$ and $$dy$$ got switched. The correct formula is:

$y-y_{1}=-\frac{1}{\frac{dy}{dx}}(x-x_{1})$

But then this notation can be misleading as the derivative should be evaluated where $$x=x_1$$.
We could use $$\frac{dy}{dx}\Big|_{x=x_1}$$ however I prefer to use $$f'(x_1)$$.

Quote:For the case y = x^4, we have

$$y-y_{1}=-\frac{1}{4x^{3}}(x-x_{1})$$

The variable in the derivative should be $$x_1$$:

$$y-y_{1}=-\frac{1}{4x_1^{3}}(x-x_{1})$$

Quote:$$(x_{1},y_{1})=(u,u^{4})$$
$$y-u^{4}=-\frac{1}{4u^{3}}(x-u)$$

Now we're back on the same road.

Quote:Thanks for posting this interesting problem!

1+

Cheers
Thomas
 « Next Oldest | Next Newest »

 Messages In This Thread Brain Teaser - Area enclosed by a parabola and a line - CR Haeger - 09-11-2015, 04:57 PM RE: Brain Teaser - Area enclosed by a parabola and a line - Gerson W. Barbosa - 09-13-2015, 12:17 AM RE: Brain Teaser - Area enclosed by a parabola and a line - CR Haeger - 09-13-2015, 01:19 PM RE: Brain Teaser - Area enclosed by a parabola and a line - Claudio L. - 09-13-2015, 01:35 AM RE: Brain Teaser - Area enclosed by a parabola and a line - Gerson W. Barbosa - 09-13-2015, 02:40 AM RE: Brain Teaser - Area enclosed by a parabola and a line - Thomas Klemm - 09-13-2015, 04:23 PM RE: Brain Teaser - Area enclosed by a parabola and a line - Gerson W. Barbosa - 09-15-2015, 03:29 AM RE: Brain Teaser - Area enclosed by a parabola and a line - fhub - 09-15-2015, 11:56 AM RE: Brain Teaser - Area enclosed by a parabola and a line - Gerson W. Barbosa - 09-15-2015, 01:30 PM RE: Brain Teaser - Area enclosed by a parabola and a line - fhub - 09-15-2015, 02:59 PM RE: Brain Teaser - Area enclosed by a parabola and a line - Gerson W. Barbosa - 09-15-2015, 04:18 PM RE: Brain Teaser - Area enclosed by a parabola and a line - fhub - 09-15-2015, 05:00 PM RE: Brain Teaser - Area enclosed by a parabola and a line - Gerson W. Barbosa - 09-15-2015, 05:08 PM RE: Brain Teaser - Area enclosed by a parabola and a line - fhub - 09-15-2015, 09:42 PM RE: Brain Teaser - Area enclosed by a parabola and a line - Bunuel66 - 09-13-2015, 10:06 PM RE: Brain Teaser - Area enclosed by a parabola and a line - Gerson W. Barbosa - 09-16-2015, 02:19 AM RE: Brain Teaser - Area enclosed by a parabola and a line - CR Haeger - 09-14-2015, 03:57 PM RE: Brain Teaser - Area enclosed by a parabola and a line - Bunuel66 - 09-14-2015, 05:08 PM RE: Brain Teaser - Area enclosed by a parabola and a line - Bunuel66 - 09-14-2015, 05:51 PM RE: Brain Teaser - Area enclosed by a parabola and a line - eried - 09-14-2015, 08:32 PM RE: Brain Teaser - Area enclosed by a parabola and a line - CR Haeger - 09-14-2015, 10:06 PM RE: Brain Teaser - Area enclosed by a parabola and a line - CR Haeger - 09-15-2015, 02:44 PM RE: Brain Teaser - Area enclosed by a parabola and a line - Gerson W. Barbosa - 09-16-2015, 02:06 AM RE: Brain Teaser - Area enclosed by a parabola and a line - Thomas Klemm - 09-16-2015 05:12 AM RE: Brain Teaser - Area enclosed by a parabola and a line - Gerson W. Barbosa - 09-16-2015, 03:09 PM RE: Brain Teaser - Area enclosed by a parabola and a line - Thomas Klemm - 09-16-2015, 03:55 PM RE: Brain Teaser - Area enclosed by a parabola and a line - Gerson W. Barbosa - 09-16-2015, 04:14 PM RE: Brain Teaser - Area enclosed by a parabola and a line - Gerson W. Barbosa - 09-18-2015, 05:51 PM RE: Brain Teaser - Area enclosed by a parabola and a line - fhub - 09-21-2015, 05:53 PM RE: Brain Teaser - Area enclosed by a parabola and a line - Gerson W. Barbosa - 09-21-2015, 06:40 PM RE: Brain Teaser - Area enclosed by a parabola and a line - Gerson W. Barbosa - 09-21-2015, 09:48 PM RE: Brain Teaser - Area enclosed by a parabola and a line - Thomas Klemm - 09-18-2015, 08:20 PM

User(s) browsing this thread: 1 Guest(s)