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Plz Help!!urgent Need Of Solutions To Some Maths Problems,thanks As U Help by cole01: 3:12pm On Jun 12
Good afternoon people, am really in need of solutions to some questions and I'll be glad if my thread is being moved to FP
Lalasticlala, Mynd44, thanks

Re: Plz Help!!urgent Need Of Solutions To Some Maths Problems,thanks As U Help by Regiomontanus(m): 5:36pm On Jun 12
@cole01

This exercise requires a good knowledge of calculus. Here are the answers.

1) The domain is the interval (0, 1].

2) The limit does not exist.

3) The gradient at (a, ρ) is -b²/aρ

4) F'(x) = 24

5) The slope is undefined. Either it has a vertical tangent line of none at all. I will investigate the behaviour of the function later to conclude which is it.
Edit: the tangent line doesn't exist.

6) a = 1

7) ½x³e2x - ¾x²e2x + ¾xe2x - ⅜e2x + C

8} a = e and b = 1, e is the Euler's constant ie. the base of the natural logarithmic function.

9) f(x) = x, a = 3 & b = -1

10) n = 1
Re: Plz Help!!urgent Need Of Solutions To Some Maths Problems,thanks As U Help by cole01: 6:00am On Jun 13
Regiomontanus:
@cole01

This exercise requires a good knowledge of calculus. Here are the answers.

1) The domain is the interval (0, 1].

2) The limit does not exist.

3) The gradient at (a, ρ) is -b²/aρ

4) F'(x) = 24

5) The slope is undefined. Either it has a vertical tangent line of none at all. I will investigate the behaviour of the function later to conclude which is it.
Edit: the tangent line doesn't exist.

6) a = 1

7) ½x³e2x - ¾x²e2x + ¾xe2x - ⅜e2x + C

8} a = e and b = 1, e is the Euler's constant ie. the base of the natural logarithmic function.

9) f(x) = x, a = 3 & b = -1

10) n = 1
Regiomontanus
Thank you very much sir, plz can I just get the picture of the solvings, I remain grateful
Re: Plz Help!!urgent Need Of Solutions To Some Maths Problems,thanks As U Help by cole01: 9:29pm On Jun 13
[quote author=Regiomontanus post=79267919]@cole01
This exercise requires a good knowledge of calculus. Here are the answer please I've been waiting Sir, really need it urgently
Re: Plz Help!!urgent Need Of Solutions To Some Maths Problems,thanks As U Help by Regiomontanus(m): 9:45pm On Jun 13
cole01:
please I've been waiting Sir, really need it urgently
I have been busy. I will send them very soon. I need to eat first.
Re: Plz Help!!urgent Need Of Solutions To Some Maths Problems,thanks As U Help by cole01: 10:10pm On Jun 13
Regiomontanus:
I have been busy. I will send them very soon. I need to eat first.
ok sir, thanks for ur reply
Re: Plz Help!!urgent Need Of Solutions To Some Maths Problems,thanks As U Help by cole01: 8:23am On Jun 14
Regiomontanus:
I have been busy. I will send them very soon. I need to eat first.
Sir I've been waiting, submitting by 10am
Re: Plz Help!!urgent Need Of Solutions To Some Maths Problems,thanks As U Help by Regiomontanus(m): 9:12am On Jun 14
cole01:

Sir I've been waiting, submitting by 10am
Sorry, my day has been tight.

1) if f(x) = g(x)h(x), then the domain of f(x) is the intersection of the domains of g(x) and h(x).
The domain of g(x) = (1 - x)½ is (-∞, 1] and the domain of h(x) = ln x is the set of all positive numbers ie. the interval (0, ∞).
Therefore the domain of f(x) = g(x)h(x) = (1 - x)½ ln x is (0, 1].

Typing...

cole01
Re: Plz Help!!urgent Need Of Solutions To Some Maths Problems,thanks As U Help by Regiomontanus(m): 9:20am On Jun 14
2) the limit doesn't exist because on both sides of 0, the function approaches two different numbers (-1 from the left and 1 from the right).

3) Find dy/dx for b²x² + a²y² = b²a² using implicit differentiation. We have 2b²x + 2a²y(dy/dx) = 0.
Hence, dy/dx = -b²x/a²y. @ (a, p), dy/dx = -b²/ap

Typing...

cole01
Re: Plz Help!!urgent Need Of Solutions To Some Maths Problems,thanks As U Help by Regiomontanus(m): 9:30am On Jun 14
4) if F(x) = f(g(x)) then by the chain rule of differentiation, F'(x) = f'(g(x))g'(x). So F'(5) = f'(g(5))g'(5)
if g(5) = -2 then f'(g(5)) = f'(-2) = 4 and g'(5) = 6. Therefore, F'(5) = (4)(6) = 24

typing ...

cole01
Re: Plz Help!!urgent Need Of Solutions To Some Maths Problems,thanks As U Help by Regiomontanus(m): 9:44am On Jun 14
5) Using implicit differentiation to find dy/dx for cos x + sin y = 1 leads to -sin x + cos y (dy/dx) = 0
Therefore dy/dx = sin x / cos y , at (π/2, π/2) dy/dx = 1/0 = udf
The tangent line is nonexistent.

6) The points of intersection of both graphs are x = 0 and x = 1 and on the interval [0, 1], y1 = x2 - x + 3 is greater than or equal to y2 = x3 - x + 3. So integrate y1 - y2 = x2 - x3 from 0 to 1 and you will get 1/12.
therefore a = 1

typing...

cole01
Re: Plz Help!!urgent Need Of Solutions To Some Maths Problems,thanks As U Help by Brunicekid(m): 9:47am On Jun 14
Mathematics, the father of all subjects... Argue with your keypads.

Meanwhile, i will try and solve the questions.

1 Like 1 Share

Re: Plz Help!!urgent Need Of Solutions To Some Maths Problems,thanks As U Help by Regiomontanus(m): 9:56am On Jun 14
7) You will have to use integration by parts repeatedly to get the answer. I can,t write them as I am on a bus.

8} An antiderivative of the integrand f(x) = (cos x)esin x is F(x) = esin x because F'(x) = f(x). Using the first fundamental theorem of calculus, the definite integral is esin π/2 - esin 0 = e1 - e0 = e - 1.
Therefore a = e and b = 1

typing...

cole01
Re: Plz Help!!urgent Need Of Solutions To Some Maths Problems,thanks As U Help by Regiomontanus(m): 10:11am On Jun 14
sorry that this is coming too late,

9) using long division (x3[sup]+x[sup]2+7)/(x2+x-2) can be written as x + [(2x+7)/(x2+x-2)]
Apply the method of partial fraction to the proper rational expression ,
(2x+7)/(x2+x-2) = (2x+7)/[(x-1)(x+2)] = A/(x-1) + B/(x+2)
Multiply both sides with (x-1)(x+2), 2x+7 = A(x+2) + B(x-1). If x = 1 , A = 3 and if x = -2, B = -1. So (x3+x2+7)/(x2+x-2) = x + 3/(x-1) + -1/(x+2).
therefore f(x) = x , A = 3 and B = -1

typing...
Re: Plz Help!!urgent Need Of Solutions To Some Maths Problems,thanks As U Help by Regiomontanus(m): 10:13am On Jun 14
cole01, I am sorry for not sending the solutions on time. I was busy and exhausted. sad
Re: Plz Help!!urgent Need Of Solutions To Some Maths Problems,thanks As U Help by Regiomontanus(m): 10:18am On Jun 14
10) nx2 + 2x = 4 + 2x at x = 2 to ensure continuity. 4n + 4 = 8. therefore n = 1


the end.

cole01
Re: Plz Help!!urgent Need Of Solutions To Some Maths Problems,thanks As U Help by cole01: 9:53pm On Jun 14
Regiomontanus:
10) nx2 + 2x = 4 + 2x at x = 2 to ensure continuity. 4n + 4 = 8. therefore n = 1


the end.

cole01
Thanks Sir, am so so grateful for every thing,thanks
Re: Plz Help!!urgent Need Of Solutions To Some Maths Problems,thanks As U Help by Regiomontanus(m): 7:09am On Jun 15
cole01:

Thanks Sir, am so so grateful for every thing,thanks
Were you able to copy them and support?

In case you have any maths questions, mention me. If I can solve them, I will and I will send the workings and answers as fast as possible. wink

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