Recent content by JC3187

Then what do i do?

Hi guys, What is the best way to sketch 0 = x2 - 2x + 4y2 And 8 = x2 - 2x + 4y2 ? How do I sketch these two and how do I know they're both ellipses? Thank you.

Hi guys, I am confused from what I know the max. value of directional derivative at a point is the length of the gradient vector ∇f or grad. f? Why does the answer in my book of a question say that Max. val of Duf = (√3145)/5 when ∇f = (56/5) i- (3/5) j ? Thanks

I thought so too, thanks!

Hi guys, Question is: Find the slopes of the curves of intersection of surface z = f(x,y) with the planes perpendicular to the x-axis and y-axis respectively at the given point. z = 2x2y ...at (1,1). fx(x,y) = 4xy ∴ Slope = 4 fy(x,y) = 2x2 ∴ Slope = 2 Is this wrong? Answer...

Things are now clear, Thank you all!

Still am confused... Why is it between 0 and 9?

Natural domain: 9 - x2 - y2 > 0 x2 + y2 < 9 How more precise can I be with this...

f(x,y) = ln(9 - x2 - y2) Domain I got: (x, y) in R2 such that x2 + y2 < 9 How do I find the range from the domain? Wouldn't it be all positive numbers of ln such that it is less than ln(9)? Answer says less than or equal to 9, I don't get why. Any input is appreciated!

Yes sorry That is what I meant. How do you derive it from the original equation? x=2sint, y=sin(2t) without dividing by x?

Hi guys, I have done what I can with the following: Given a parametric curve x = xsint, y = sin(2t) where t is in R. Find an implicit equation of this curve. MY ANSWER: y = 2costsint = costx Therefore sint = x/2, cost = y/x sin^2(t) + cos^2(t) = x^2 / 4 + y^2 / x^2 = 1 Would this be...

Given z = 1 + i, Find all complex solutions to z^{2} + Conjugate:z^{2} = 0 I have come up with a way to solving this but it doesn't make any sense. would it be: z^{2} + 1-i = 0 z^{2} = -1+i Solve for all complex roots then do the same for conjugate squared?

I think i understand, so would this be correct for the following question: Re(z+2) = -1 -3 in the real axis?

Thanks for your reply, though I am still a little confused. Could you go through the working please?

Hi guys, So as title states, how would one sketch Re(iz) = 3? And an explanation would be splendid. This is what I thought: let z = a + bi i(a+bi) = -b + ai Therefore: Re(iz) = -b = 3 So Real axis = -3? Or would it be Real axis = 3 Since iz is an arbitrary complex number and...