Math Help Forum - Calculus

Math Help Forum - Calculus http://www.mathhelpforum.com/math-help en Fri, 20 Nov 2009 22:04:49 GMT vBulletin 60 http://www.mathhelpforum.com/math-help/images/MHF/misc/rss.jpg Math Help Forum - Calculus http://www.mathhelpforum.com/math-help Cylindrical Can Optimization http://www.mathhelpforum.com/math-help/calculus/115802-cylindrical-can-optimization.html Fri, 20 Nov 2009 21:58:41 GMT This is my first post and involves optimization of the most economic shape of a can. The problem verbatim is "Let's assume that most of the expense is incurred in joining the sides to the rims of the cans. If we cut the discs from hexagons as in task #4, then the total cost is proportional to

4*3^(1/3)r^2+2pirh+k(4pir+h)

where k is the reciprocal of the length that can be joined for the cost of one unit area of metal. Show that this expression is minimized when:

(V^1/3)/k= ((pih)/r)^1/3 * (2pi-h/r)/(pih/r-4*3^(1/3)

I have no idea where to begin with this one. Any help is much appreciated. ]]> Calculus heebee http://www.mathhelpforum.com/math-help/calculus/115802-cylindrical-can-optimization.html Computing Residue http://www.mathhelpforum.com/math-help/calculus/115789-computing-residue.html Fri, 20 Nov 2009 20:53:15 GMT I need to compute the residue for $\frac{e^{-z}}{(z-1)^2}$ . I'm going to be using it for Cauchy's residue theorem to evaluate the integral around the circle |z| = 3, so there is obviously a singularity at z=1. I'm confused how to manipulate the fraction and bring in series so that I can see what the coefficient on the $\frac{1}{z-1}$ term. Thank you. ]]> Calculus azdang http://www.mathhelpforum.com/math-help/calculus/115789-computing-residue.html Differentiation problems http://www.mathhelpforum.com/math-help/calculus/115778-differentiation-problems.html Fri, 20 Nov 2009 20:11:12 GMT Hey i am having a bit of trouble with these differentiation problems; 1. Find the equation to the tangent to y=e^-x, at the point where x = 1 2. Find the equation to the tangent to y= ln(2-x) at the point where x = -1 3. The tangent at x = 1 to y = x^2e^x cuts the x and y axis at A and B... Hey i am having a bit of trouble with these differentiation problems;

1. Find the equation to the tangent to y=e^-x, at the point where x = 1
2. Find the equation to the tangent to y= ln(2-x) at the point where x = -1
3. The tangent at x = 1 to y = x^2e^x cuts the x and y axis at A and B respectively. Find the coordinate of A and B
4. Find the equation of the normal to y = ln √ x at the point where y = -1

Im not sure about any of these but for the first 2 i think you have to differentiate first but im nt really sure..

thanks! ]]> Calculus Jampop http://www.mathhelpforum.com/math-help/calculus/115778-differentiation-problems.html Find the integral http://www.mathhelpforum.com/math-help/calculus/115772-find-integral.html Fri, 20 Nov 2009 18:31:17 GMT _Image: http://i47.tinypic.com/zsn3bd.jpg _

]]> Calculus racewithferrari http://www.mathhelpforum.com/math-help/calculus/115772-find-integral.html Do I need to change this into parametric form? http://www.mathhelpforum.com/math-help/calculus/115771-do-i-need-change-into-parametric-form.html Fri, 20 Nov 2009 18:31:10 GMT I need to find the points on:

$x^2+\frac{y^2}{4}+\frac{z^2}{9}=1$

where the tangent line is parallel to:

$x+2y+z=0$

This is what I've done:

$\langle 2x, \frac{y}{4}, \frac{2z}{9} \rangle \cdot \langle 1,2,1 \rangle =0$

$=2x+y+\frac{2z}{9}=0$

Not sure what to do now... do I have to change this to parametric form? Should I have changed it first? ]]> Calculus MathSucker http://www.mathhelpforum.com/math-help/calculus/115771-do-i-need-change-into-parametric-form.html Calculus Intergral......Evaluating the Riemann sum http://www.mathhelpforum.com/math-help/calculus/115770-calculus-intergral-evaluating-riemann-sum.html Fri, 20 Nov 2009 18:30:13 GMT Image: http://i47.tinypic.com/skxqh5.jpg

]]> Calculus racewithferrari http://www.mathhelpforum.com/math-help/calculus/115770-calculus-intergral-evaluating-riemann-sum.html Another line integral question.... http://www.mathhelpforum.com/math-help/calculus/115769-another-line-integral-question.html Fri, 20 Nov 2009 18:26:38 GMT Evaluate the line integral directly, WITHOUT using Green's theorem.

Integral of (x-y)dx+(x+y)dy where C is the circle with center the origin and radius 2.

I have to show that both methods give me the same answer. I know how to do it with Green's theorem...but not otherwise. ]]> Calculus daskywalker http://www.mathhelpforum.com/math-help/calculus/115769-another-line-integral-question.html <![CDATA[L'Hospital's rule]]> http://www.mathhelpforum.com/math-help/calculus/115765-lhospitals-rule.html Fri, 20 Nov 2009 17:55:27 GMT 0+ (tan 2x)^x 2. lim x-> 1 (2 - x)^tan((pi)x/2)]]> Can anyone explain the procedures in solving these two problems using L'Hospital's rule?

1. lim x-> 0+ (tan 2x)^x

2. lim x-> 1 (2 - x)^tan((pi)x/2) ]]> Calculus Eternal http://www.mathhelpforum.com/math-help/calculus/115765-lhospitals-rule.html Newton-Raphson Theorem Third Repetition Confirmation http://www.mathhelpforum.com/math-help/calculus/115758-newton-raphson-theorem-third-repetition-confirmation.html Fri, 20 Nov 2009 17:34:21 GMT Hi, Can anyone confirm for me that the third Newton-Raphson repetition of f(x)=e^x+10x-3 at x=0 is approximately 0.18025? Hi,

Can anyone confirm for me that the third Newton-Raphson repetition of $f(x)=e^x+10x-3$ at x=0 is approximately 0.18025? ]]> Calculus Kataangel http://www.mathhelpforum.com/math-help/calculus/115758-newton-raphson-theorem-third-repetition-confirmation.html Taylor Polynomial Confirmation http://www.mathhelpforum.com/math-help/calculus/115757-taylor-polynomial-confirmation.html Fri, 20 Nov 2009 17:28:20 GMT Hi, Can anyone confirm for me that third Taylor Polynomial of f(x)=\sqrt{1-x} at x=0 is 1-\frac{1}{2}x-\frac{1}{8}x^2-\frac{1}{16}x^3 Or P3(0)=1? Hi,

Can anyone confirm for me that third Taylor Polynomial of $f(x)=\sqrt{1-x}$ at x=0 is $1-\frac{1}{2}x-\frac{1}{8}x^2-\frac{1}{16}x^3$

Or P3(0)=1? ]]> Calculus Kataangel http://www.mathhelpforum.com/math-help/calculus/115757-taylor-polynomial-confirmation.html Fundamental Theorem of Calculus to find the derivative of the function http://www.mathhelpforum.com/math-help/calculus/115756-fundamental-theorem-calculus-find-derivative-function.html Fri, 20 Nov 2009 17:28:06 GMT Image: http://i45.tinypic.com/25irwir.jpg (http://i50.tinypic.com/23keykn.jpg)

]]> Calculus racewithferrari http://www.mathhelpforum.com/math-help/calculus/115756-fundamental-theorem-calculus-find-derivative-function.html Surface Integral Help http://www.mathhelpforum.com/math-help/calculus/115754-surface-integral-help.html Fri, 20 Nov 2009 17:16:07 GMT The figure shows the surface created when the cylinder\ y^2 + z^2 = 1\ intersects\ the\ cylinder\ x^2 + z^2 = 1\ Find\ the\ area\ of\ this\ surface. I think to find the surface integral we need to do the double integral of ru cross rv, with respect to du and dv respectively. However, im not even... The figure shows the surface created when the $cylinder\ y^2 + z^2 = 1\ intersects\ the\ cylinder\ x^2 + z^2 = 1\ Find\ the\ area\ of\ this\ surface.$

I think to find the surface integral we need to do the double integral of ru cross rv, with respect to du and dv respectively. However, im not even sure how to get to that point.

Attached Thumbnails

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]]> Calculus purplerain http://www.mathhelpforum.com/math-help/calculus/115754-surface-integral-help.html I am confused on the steps for optimization, could someone please help http://www.mathhelpforum.com/math-help/calculus/115750-i-am-confused-steps-optimization-could-someone-please-help.html Fri, 20 Nov 2009 16:36:26 GMT Here is the sample problem (but the object will change for the test): Optimization.The base b and height h of an isosceles triangle vary in such a way that its perimeter,is constant,and equal to 6. Find the maximum possible area of the triangle. What I know from this: P=B * 2S (base times... Here is the sample problem (but the object will change for the test):

Optimization.The base b and height h of an isosceles triangle vary in such
a way that its perimeter,is constant,and equal to 6. Find the maximum possible area of the triangle.

What I know from this:
P=B * 2S (base times the 2 sides)
P=6
A=BH (base times height)

From the question I also think that I will be needing to find f' and f'' to find the maximimum area for the triangle, but I am not sure on that.

I always get confused on the steps to work through optimization word problems. Can someone please help? I understand more if there is a step by step process to solve something. ]]> Calculus operaphantom2003 http://www.mathhelpforum.com/math-help/calculus/115750-i-am-confused-steps-optimization-could-someone-please-help.html Partial fraction question http://www.mathhelpforum.com/math-help/calculus/115743-partial-fraction-question.html Fri, 20 Nov 2009 15:43:41 GMT I need help solving: integral of (20x-30) / (x(x-2)(x^2-2x+5)) If I try to decompose it; I will have LHS from above = (A/x)+(B/x-2) + ? I need help solving:

integral of (20x-30) / (x(x-2)(x^2-2x+5))

If I try to decompose it;

I will have

LHS from above = (A/x)+(B/x-2) + ?

Stuck here.
]]> Calculus shadow85 http://www.mathhelpforum.com/math-help/calculus/115743-partial-fraction-question.html Derivatives http://www.mathhelpforum.com/math-help/calculus/115739-derivatives.html Fri, 20 Nov 2009 14:40:07 GMT Find derivative dy/dx if a) y=tan^-1(1/2x) b) y=4^(-x+3) thanks! Find derivative dy/dx if

a) y=tan^-1(1/2x)

b) y=4^(-x+3)

thanks! ]]> Calculus live_laugh_luv27 http://www.mathhelpforum.com/math-help/calculus/115739-derivatives.html