Lecture7 - use power rule image depends on parameter T -...

Info iconThis preview shows pages 1–15. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: use power rule image depends on parameter T - let it go to infinity - original integral is equal to 1/2 if one diverges, altogether the area is infinite function defined for integral - is continuous infinite area (looking at the function of 1/x^p shifted ( a constant) when less than one we know everything about this integral not of the form int2 to 5(dx/(x-2)^2) this integral converges - the exponent p is 1/2 which is less than one from E to 5, the function is defined trying to determine behaviour at 2 function blows up at x=2 antiderivative goes to zero is of the form that we know about replaced 0 type 2 the exponent is greater than one - this is how we can check whether our answer is right/wrong function blows up at x=2 - therefore we must isolate this point with the variable E want to know if it converges/ diverges sum of two integrals definite integral if this is shown - it is enough to prove that the entire integral diverges and therefore has infinite area split into two type 2 type 1 converges when p>1 Type 2 is this integral divergent/convergent problem at x=0 so we isolate the problem point integrate by parts if limit is finite number = convergence of the original integral plug in upper and lower limit of integral don't know the answer repositioning to be able to use L'Hopital's rule type 1 - infinite interval of integration bell shape split into two when x goes to + or - infinity, the function goes to pi/2 ...
View Full Document

Page1 / 15

Lecture7 - use power rule image depends on parameter T -...

This preview shows document pages 1 - 15. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online