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pmann (m)
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Calculus which comprises of both differentiation and integration is the bed rock of engineering, technology and some sciences. If you intend studying any of the above discipline mostly engineering and technology, a very sound knowledge of calculus is required of you. You can hardly cope in engineering or technology if you don't have a sound knowledge of calculus. infact there is a level you will get to that you will need calculus in almost every area of your discipline. Please do not joke with calculus for it is the bed rock of engineering and all related fields. bring all your question let reason together so that we can find solutions to them all.
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pmann (m)
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Can any one find d2y/dx2 for the following if:
1. y = 4x4 + 10x2
2. y = (5x3 - 50x)4
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ebaneo (m)
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it is too simple. we need tough question. the first one just differantiate it to get dy|dx and differiante it again to get d2y|dx2.
the second one expand the bracket using pascal triangle, after that apply rule 1. QED
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Ibime (m)
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^^^OK, you like tough Calculus questions? Oya solve this one:
An open-ended rectangular water tank of diameter 3.1m contains water which flows out through a tap at the bottom. The taphole has a diameter of 0.075m. The height of the water is 3.5m at time t0 and take the density of the water as 7100Kgm-3. If the velocity at the taphole is V = sqrt(2gh) where h(t) is the instantaneous height and gravity is 9.81ms-2, find the time taken to empty the container.
Hint: You need to integrate dh/dt
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MyTempID
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it is too simple. we need tough question. the first one just differantiate it to get dy|dx and differiante it again to get d2y|dx2.
the second one expand the bracket using pascal triangle, after that apply rule 1. QED
I beg to differ. For the second one, expansion using pascal's triangle would just make things more complicated than they should be. Chain rule is enough to differentiate that function. |
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MyTempID
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Can any one find d2y/dx2 for the following if:
1. y = 4x4 + 10x2
2. y = (5x3 - 50x)4
y = 4x 4 + 10x 2dy/dx =16x 3 + 20x d 2y/dx 2 = 48x 2 + 20 (5x 3 - 50x) 4dy/dx = 4(5x 3 - 50x) 3*(15x 2-50) dy/dx = (5x 3 - 50x) 3*(60x 2-200) d 2y/dx 2 = [3*(5x 3-50x) 2*(15x 2-50)*(60x 2-200)] + 120x*(5x 3 - 50x) 3 |
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bawomolo (m)
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ah well u guys want a tough question.
find the maximum value of cosine(x^2-y^2) if x^2+y^2=1
find the value of the closed integral of (ydx + xdy + zdz) if x^2+y^2 = z , z<= 1
find the area of a circle if x^2 + y^2=4
find a vector field whose divergence is 1 + 3y^2 + xy
find the curl of x^2yi + 2xj + 3zyK
find the path integral if f = x^2+y^2 + z and c(t) = (sint,cost,t) t range from [0,1]
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Ibime (m)
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ah well u guys want a tough question.
find the maximum value of cosine(x^2-y^2) if x^2+y^2=1
Max cosine = Cosine of zero = 1. Using that logic and knowing that x 2 or y 2 cannot be negative, I would say that both x 2 and y 2 are definitely less than 1. So . . . . . . . If x 2 = 0.5 and y 2 = 0.5, then x 2 - y 2 = 0 and cosine(0) = 1 Tentatively, I will suggest that the max value of cosine(x 2-y 2) = 1 I could be wrong. It sounds too obvious to be true. |
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Ibime (m)
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find the area of a circle if x^2 + y^2=4
If this is a circle with centre (0,0), then the radius is 2, just apply pie x r 2or 4 x pie = 88/7 = 12.5714m 2 |
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bawomolo (m)
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we technically are supposed to solve them using calculus
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pmann (m)
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you guys are great mathematicians.
please help out with the following questions.
1. integrate (x2 - 16)1/2dx
2. integrate sin4xdx
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Ibime (m)
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we technically are supposed to solve them using calculus
O-boy, I don almost forget all the methods for Calculus except Taylor's theorem because now I mostly deal with P.D.E's and na computer we dey use solve everything so I got to use Ibo man sense solve the questions. |
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bawomolo (m)
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you guys are great mathematicians.
please help out with the following questions.
1. integrate (x2 - 16)1/2dx
2. integrate sin4xdx
damn this are tough ones, got to use a table lol |
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ebaneo (m)
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pmann, for the second one try using De Moivre"s theorem in complex numbers.
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MyTempID
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they're not so bad. here's one, i'll work on the other one later.
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