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.

Can any one find d²y/dx² for the following if:

1. y = 4x⁴ + 10x²

2. y = (5x³ - 50x)⁴

^^^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

ebaneo:

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.

pmann:

Can any one find d²y/dx² for the following if:

1. y = 4x⁴ + 10x²

2. y = (5x³ - 50x)⁴

y = 4x⁴ + 10x²
dy/dx =16x³ + 20x
d²y/dx² = 48x² + 20


(5x³ - 50x)⁴
dy/dx = 4(5x³ - 50x)³*(15x²-50)
dy/dx = (5x³ - 50x)³*(60x²-200)

d²y/dx² = [3*(5x³-50x)²*(15x²-50)*(60x²-200)] + 120x*(5x³ - 50x)³

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]

bawomolo:

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 x² or y² cannot be negative, I would say that both x² and y² are definitely less than 1.

So . . . . . . .

If x² = 0.5 and y² = 0.5, then x² - y² = 0 and cosine(0) = 1

Tentatively, I will suggest that the max value of cosine(x²-y²) = 1

I could be wrong. It sounds too obvious to be true.

bawomolo:


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 r²

or 4 x pie

= 88/7

= 12.5714m²

we technically are supposed to solve them using calculus

you guys are great mathematicians.

please help out with the following questions.

1. integrate (x² - 16)^1/2dx

2. integrate sin⁴xdx

bawomolo:

we technically are supposed to solve them using calculus

O-boy, I don almost forget all the methods for Calculus except Taylor's theorem cos 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.

pmann:

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

they're not so bad. here's one, i'll work on the other one later.

I need help on diesel engines( those with 4 and 6 cylinder for a start). My question is what really causes the upward and downward movement of the piston i.e what causes combustion in diesel engines? How does gasoline engines differs from diesel engines?

Dear Friends,
Please, help solve this maths for me:


1. Show that (1 + sin x )(1 + secant x) = Tan x
(1 + cosine x)(1 + cosecant x)

(please, note: it is numerators (1 + sin x)(1 + secant x) over denominators 1 + cosine x) (1 + cosecant x) = Tan x)

2. Express the following angles in degrees
(i) 370 (ii) -430 10' (i.e. 10' is 10 seconds)

3. Express the following angle sin radiant
(i) 21 radiant (ii) п radiant (i.e. pie over 12)
12

Please, give details so I can learn, if possible send to my email: challomkindy@yahoo.co.uk

Many thanks.

Kindy

pmann:

I need help on diesel engines( those with 4 and 6 cylinder for a start). My question is what really causes the upward and downward movement of the piston i.e what causes combustion in diesel engines? How does gasoline engines differs from diesel engines?

diesel engines are compression ignition engines that self-ignite. gasoline engines are usually spark-ignition engines that require a spark plug to combustion.  diesel engines have hire fuel efficiency while gasoline engines have higher volumetric efficiency.  gasoline engines use an homogenous mixture diesel engine while use an heterogenous mixture.  diesel engines have an higher compression ratio(16:1 to 24:1) than gasoline engine.  i believe diesel engines run at an equivalent air-fuel ratio while gasoline engines are usually lean(more air than fuel). diesel engines use fuel with high cetane numbers while gasoline engines use fuel with high octane numbers.

Kindy:

Dear Friends,
Please, help solve this maths for me:


1. Show that (1 + sin x )(1 + secant x) = Tan x
(1 + cosine x)(1 + cosecant x)

(please, note: it is numerators (1 + sin x)(1 + secant x) over denominators 1 + cosine x) (1 + cosecant x) = Tan x)

2. Express the following angles in degrees
(i) 370 (ii) -430 10' (i.e. 10' is 10 seconds)

3. Express the following angle sin radiant
(i) 21 radiant (ii) п radiant (i.e. pie over 12)
12

Please, give details so I can learn, if possible send to my email: challomkindy@yahoo.co.uk

Many thanks.

Kindy
0803 557 8818
challomkindy@yahoo.co.uk

I think you meant

2. Express the following angles in radians
(i) 370 (ii) -430 10' (i.e. 10' is 10 seconds)

3. Express the following angles in degrees
(i) 21 radiant (ii) п radiant (i.e. pie over 12)
12


I'll provide solutions soon enough.

Here

Calculus must nt die...

More calculus questions pls.

Try this simple1 y=x^4 +5x^3 -6x^2 +7x -3

compute its diffrential coefficient
hence or other wise obtain the equation of tangent to the curve and normal.

benbuks: Try this simple1 y=x^4 +5x^3 -6x^2 +7x -3

compute its diffrential coefficient
hence or other wise obtain the equation of tangent to the curve and normal.

..who is tryin dis.?

Ibime: ^^^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

...I dont really fink this is tough enough.....

Ibime: ^^^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

...I dont really fink this is tough enough.....

Nice thread! joining in...greetings to all the Engineers/Engineering students, Mathematicians/Math gurus and other CALCULUS lovers on the thread!

benbuks: Try this simple1 y=x^4 +5x^3 -6x^2 +7x -3

compute its diffrential coefficient
hence or other wise obtain the equation of tangent to the curve and normal.

equatn at point wat?

benbuks: Try this simple1 y=x^4 +5x^3 -6x^2 +7x -3

compute its diffrential coefficient
hence or other wise obtain the equation of tangent to the curve and normal.

..sorry at x=-2

pls help me and solved dis one. show dat 1-cosx=2sin^21/2x

Ok, where are the calculus gurus na, safe the life of this thread na..

How do i master sophomore's dream pls.?