Recent content by shocklightnin

Homework Statement Is there such a number b such that lim x->-2 (3x^2+bx+b+3)/(x^2+x-2) exists? If so, find b and the limit.Homework Equations lim x->-2 (3x^2+bx+b+3)/(x^2+x-2)The Attempt at a Solution for the denominator we have zeroes at x = 1 and -2. so we need to get rid of the -2 part...

good grief i had x^2(x-5) copied on my paper. goodness, nevermind haha. :$$

Homework Statement use implicit differentiation to find an equation of the tangent line to the curve a the given point. y^2(y^2-4) = x^2(x^2-5) at (0,-2) Homework Equations y^2(y^2-4) = x^2(x^2-5) The Attempt at a Solution I got dy/dx to be (3x^2-10x)/(4y^3-8y) but...

thanks to both! and nope, book def. says '(2-x^2) and not (2-x)^2, must be a printing error either in book or ans. key, but thank you!

Homework Statement We're given a piecewise function g(x) = { x if x < 1 3 if x = 1 2-x^2 if 1<x<=2 x-3 if x > 2 ] and were asked: lim x-> 2- Homework Equations 2-x^2 if 1<x<=2 x-3 if x > 2 The Attempt at a Solution when i drew it out i was getting that the answer...

ooh right right! so that's why its -ve infinity. ah thanks, got it now :P

positive..?

Homework Statement lim x->pi- cot(x) Homework Equations cot(x) = cos(x)/sin(x) The Attempt at a Solution so substituting pi into: cot(pi) = cos(pi)/sin(pi) = -1/0 so you have a negative over 0, approaching from the -ve side of pi wouldn't it be +infinity? why is it -infinity...

Ohhh just got the mistake. Great, thank you for your help and patience!

i already know the answer is that the function f is decreasing on (-infty, -0.345 ) U (2.645 ,+infty ) and increasing on ( -0.345 , 2.645). I am just not sure at how they arrived to it in my profs notes >.< we do the table method where its like: -0.345 2.645...

but if i include it it shows that the function is increasing over intervals (-infinity,-0.345) U (2.645,+infinity) and decreasing on (-0.345,2.645). however i know that -0.345 is a relative minimum, and if those intervals hold, it becomes a relative maximum...

Homework Statement Hi I have an equation as follows: f(x) = (2x-2.3)/(2x-5.29)^2 what i got for the derivative was: f'(x) = (-1.38-4x)/(2x-5.29)^3 Homework Equations f(x) = (2x-2.3)/(2x-5.29)^2 f'(x) = (-1.38-4x)/(2x-5.29)^3 The Attempt at a Solution what i got for the...

RoshanBBQ, thanks! Completely slipped my mind that sometimes we have to apply L'H more than once.

Homework Statement This was a question from our lecture notes, just not sure how the prof arrived at the answer. lim x->infinity (lnx)^2/x Homework Equations lim x->infinity (lnx)^2/x lim x->infinity 2lnx/x The Attempt at a Solution so both the numerator and denominator are...

Yeah, typing it out defs helped. Alright, just going to leave it then.