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#1 2013-05-14 03:01:37

ShivamS
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Single-var Calculus (and otherwise)

Some problems...one at a time.

Suppose the integral was already performed on an equation. What is the simplified answer if you now take the integral from 0 to 1 for the following integrated equation:

8x^3 + 3x^2 - 4x + C


I got 7.


I have discovered a truly marvellous signature, which this margin is too narrow to contain. -Fermat
Give me a lever long enough and a fulcrum on which to place it, and I shall move the world. -Archimedes
Young man, in mathematics you don't understand things. You just get used to them. - Neumann

#2 2013-05-14 03:57:18

anonimnystefy
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Re: Single-var Calculus (and otherwise)

7 is correct.


The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

#3 2013-05-14 03:59:43

ShivamS
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Re: Single-var Calculus (and otherwise)

Consider 'x' to be a variable. What is the derivative of 12x^4 + 10x^3 - 5x^2 + 16 with respect to x?

I get 48x^3 + 30x^2 - 10x

Also:

Consider 'x' to be a variable. What is the integral of 18x^2 - 10x + 3 with respect to x? Pick the most correct solution.

I get  6x^3 - 5x^2 + 3x + C


I have discovered a truly marvellous signature, which this margin is too narrow to contain. -Fermat
Give me a lever long enough and a fulcrum on which to place it, and I shall move the world. -Archimedes
Young man, in mathematics you don't understand things. You just get used to them. - Neumann

#4 2013-05-14 04:02:42

anonimnystefy
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Re: Single-var Calculus (and otherwise)

Both are correct! Good work! smile


The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

#5 2013-05-14 04:07:31

ShivamS
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Re: Single-var Calculus (and otherwise)

Thank-you; I just thought I needed some extra practive before the exams. After that, I should be much more relaxed... Anyways, I will post some more later.

Last edited by ShivamS (2014-03-10 03:12:35)


I have discovered a truly marvellous signature, which this margin is too narrow to contain. -Fermat
Give me a lever long enough and a fulcrum on which to place it, and I shall move the world. -Archimedes
Young man, in mathematics you don't understand things. You just get used to them. - Neumann

#6 2013-05-14 04:12:20

anonimnystefy
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Re: Single-var Calculus (and otherwise)

You are welcome.

Okay, post the other questions when you want.


The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

#7 2013-05-22 22:33:07

ShivamS
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Re: Single-var Calculus (and otherwise)

Hi; few other simple problems. Fred is standing on the ground and throws a ball up in to the air. He observes that it falls back down to the ground after 5 seconds. What was the initial velocity of the ball? I get 0  =  -400 + 5V subscript 0 Thus initial velocity = 80ft / s


I have discovered a truly marvellous signature, which this margin is too narrow to contain. -Fermat
Give me a lever long enough and a fulcrum on which to place it, and I shall move the world. -Archimedes
Young man, in mathematics you don't understand things. You just get used to them. - Neumann

#8 2013-05-22 22:42:01

ShivamS
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Re: Single-var Calculus (and otherwise)

One more: Junita is standing on the roof of a building 192 feet tall and throws a ball up in to the air with an initial speed of 64 feet / second.

(a) Find formula for velocity and position of ball at a later time.  I get v(t) = -32t + 64 And for position: y(t) = -16t^2 + 64t +192

(b) How high does the ball go? I am getting 256 feet,

(c) When does the ball hit the ground? I think this is probably wrong, but I am getting 6 seconds.

Thank-you in advance.


I have discovered a truly marvellous signature, which this margin is too narrow to contain. -Fermat
Give me a lever long enough and a fulcrum on which to place it, and I shall move the world. -Archimedes
Young man, in mathematics you don't understand things. You just get used to them. - Neumann

#9 2013-05-22 22:42:24

anonimnystefy
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Re: Single-var Calculus (and otherwise)

I am getting 25 m/s. Which formula are you using?


The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

#10 2013-05-22 22:44:50

ShivamS
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Re: Single-var Calculus (and otherwise)

Hi Stefy; for which question are you getting that?


I have discovered a truly marvellous signature, which this margin is too narrow to contain. -Fermat
Give me a lever long enough and a fulcrum on which to place it, and I shall move the world. -Archimedes
Young man, in mathematics you don't understand things. You just get used to them. - Neumann

#11 2013-05-22 22:46:38

anonimnystefy
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Re: Single-var Calculus (and otherwise)

The one in post #7.


The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

#12 2013-05-22 22:52:38

ShivamS
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Re: Single-var Calculus (and otherwise)

I get y(t) = Integral (-32t + v subscript 0)dt = -16t^2 + v subscript 0 t + C

So y(t) = -16t^2 + v0t   (o = subscript)

So 0 = -16 * 5^2 + initial velocity * 5 = -400 + 5 (initial velocity) = -400 + 5 initial velocity

Solving gives us V0 = initial velocity = 80 ft / second


I have discovered a truly marvellous signature, which this margin is too narrow to contain. -Fermat
Give me a lever long enough and a fulcrum on which to place it, and I shall move the world. -Archimedes
Young man, in mathematics you don't understand things. You just get used to them. - Neumann

#13 2013-05-22 23:01:22

anonimnystefy
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Re: Single-var Calculus (and otherwise)

Shivamcoder3013 wrote:

y(t) = Integral (-32t + v subscript 0)dt

How'd you get this?


The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

#14 2013-05-22 23:05:44

ShivamS
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Re: Single-var Calculus (and otherwise)

Similar to the problem in post 8. ground level will be position 0, up will be the positive direction and time t=0 will be the instant when Fred first throws the ball. The acceleration due to gravity will be a = -32. Thus dv/dt = -32, so that v(t) = -32 + C. The problem does not give any information about the velocity of the ball at any time so I use v0 to represent initial velocity. AT time t = 0, I get v(t) = -32t + v0. So, as v(t) = dr/dt, y(t) = integral (-32t + v0)dt = -16t + v0t + C.


I have discovered a truly marvellous signature, which this margin is too narrow to contain. -Fermat
Give me a lever long enough and a fulcrum on which to place it, and I shall move the world. -Archimedes
Young man, in mathematics you don't understand things. You just get used to them. - Neumann

#15 2013-05-22 23:11:12

anonimnystefy
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Re: Single-var Calculus (and otherwise)

But, the acceleration due to gravity is 9.81 (or 10, if you round it up) mps.


The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

#16 2013-05-22 23:13:57

ShivamS
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Re: Single-var Calculus (and otherwise)

Well, the units in the problem were feet, and 9.81 is approximately 32 feet. Also, "Similar to the problem in post 8. ground level will be position 0, up will be the positive direction and time t=0 will be the instant when Fred first throws the ball. The acceleration due to gravity will be a = -32."


I have discovered a truly marvellous signature, which this margin is too narrow to contain. -Fermat
Give me a lever long enough and a fulcrum on which to place it, and I shall move the world. -Archimedes
Young man, in mathematics you don't understand things. You just get used to them. - Neumann

#17 2013-05-22 23:35:16

anonimnystefy
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Re: Single-var Calculus (and otherwise)

Ah, so we are both correct on the initial velocity for the one in post #7.

Let me look at the second one.


The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

#18 2013-05-22 23:37:42

ShivamS
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Re: Single-var Calculus (and otherwise)

25m is 82 feet so did you simply approximate something?


I have discovered a truly marvellous signature, which this margin is too narrow to contain. -Fermat
Give me a lever long enough and a fulcrum on which to place it, and I shall move the world. -Archimedes
Young man, in mathematics you don't understand things. You just get used to them. - Neumann

#19 2013-05-22 23:40:38

anonimnystefy
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Re: Single-var Calculus (and otherwise)

Yeah, I took g to be 10m per second squared. I am getting approximately 24.525mps with g=9.81m per second squared.


The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

#20 2013-05-22 23:41:58

ShivamS
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Re: Single-var Calculus (and otherwise)

Oh, okay. Thank-you. The second one is a bit more complicated.


I have discovered a truly marvellous signature, which this margin is too narrow to contain. -Fermat
Give me a lever long enough and a fulcrum on which to place it, and I shall move the world. -Archimedes
Young man, in mathematics you don't understand things. You just get used to them. - Neumann

#21 2013-05-23 00:19:11

anonimnystefy
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Re: Single-var Calculus (and otherwise)

I think all three are correct.


The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

#22 2013-05-23 22:28:53

ShivamS
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Re: Single-var Calculus (and otherwise)

Okay, thank you very much. I have some more but I will post them later. Actually, here are some vector calculus questions:

Determine if the vector field f(x, y,z)= x yzi+xzj+x yk has a potential in R3

I am getting that it does not have the potential.


I have discovered a truly marvellous signature, which this margin is too narrow to contain. -Fermat
Give me a lever long enough and a fulcrum on which to place it, and I shall move the world. -Archimedes
Young man, in mathematics you don't understand things. You just get used to them. - Neumann

#23 2013-05-23 22:54:22

anonimnystefy
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Re: Single-var Calculus (and otherwise)

I don't think I know what the potential of a vector is.


The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

#24 2013-05-24 22:10:37

ShivamS
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Re: Single-var Calculus (and otherwise)

http://en.wikipedia.org/wiki/Vector_potential

But thank-you anyways.


I have discovered a truly marvellous signature, which this margin is too narrow to contain. -Fermat
Give me a lever long enough and a fulcrum on which to place it, and I shall move the world. -Archimedes
Young man, in mathematics you don't understand things. You just get used to them. - Neumann

#25 2013-05-27 22:29:46

ShivamS
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Re: Single-var Calculus (and otherwise)

Thanks a lot Stefy; the midterm exam went extremely well.


I have discovered a truly marvellous signature, which this margin is too narrow to contain. -Fermat
Give me a lever long enough and a fulcrum on which to place it, and I shall move the world. -Archimedes
Young man, in mathematics you don't understand things. You just get used to them. - Neumann

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