# Search results

1. ### Proving limit of multivariable function exists

Well thanks for clarifying that up you guys. I have one more similar question with which I need some help. I've gotten a bit further with this one but not enough: I concluded that the limit equals 0 by trying a few paths (hopefully this time it was right): \lim_{\{x,y\}\to \{1,0\}} \...
2. ### Proving limit of multivariable function exists

I updated my post above, to show that I did try some other paths too. So if both limits are different, then it would mean that the limit does not exist. I guess that WA isn't perfect after all. :)
3. ### Proving limit of multivariable function exists

Hi, If we are approaching from the path x = y^3, then lim (x,y) -> (0,0) of (x^1/3)*y^2 / x+y^3 = lim (x,y) -> (0,0) of (y)*y^2 / y^3+y^3 = = lim(x,y) -> (0,0) of y^3 / 2y^3. = 1/2 That seems to make sense. However, if we use the path y=x: lim (x,y) -> (0,0) of (x^1/3)*y^2 / x+y^3 = lim...
4. ### Proving limit of multivariable function exists

Homework Statement Evaluate or show that the limit DNE. Limit as (x,y) -> (0,0) of (x^1/3)*y^2 / x+y^3. The Attempt at a Solution I tried approaching from multiple paths, and it seems that the limit is equal to 0. I used the delta-epsilon method to prove the limit but I've been stuck so far...
5. ### Proving Limits

That was extremely thorough Mathstatnoob, thank you for taking the time to post the answer. I appreciate it very much. Through your steps, I've learned how to manipulate little pieces here and there to arrive at the needed answer. :) If anyone could confirm my Q1 and Q5 solutions, I'd be...
6. ### Proving Limits

Hello everyone, I am in need of a little assistance. I have a homework assignment due soon that consists of 5 questions. Of which, I have done all but the 4th one. I did start on it but I'm not sure where to go from there. I also would like for someone to confirm my solutions for question 1 and...
7. ### Solving Equation with Negative Exponent (! thank you!)

.1^(x-1) < .1 log (.1)^(x-1) < log .1 (x-1)(log .1) < log .1 Expand and solve.
8. ### Rate of change question (pretty confusing)

I think it should be dV/dT = dH/dT * dV/dH rather than what you had, Mandeep.
9. ### Rate of change question (pretty confusing)

What was the answer you got? I got 0.071 m/s.
10. ### Verifying Trig Identities

sin^3(x)-cos^3(x) ----------------- sin(x) - cos(x) Try factoring the numerator, it may help you.
11. ### Cartesian Eq. of Plane

Oh I got it! Gee, thanks for all the kind help Rock, I appreciate it. :)
12. ### Cartesian Eq. of Plane

In that case: Ax+By+Cz+D=0 (5)(2)+(-4)(-1)+7(8)+D=0 10+4+56+D=0 D=-70 Therefore, the Cart. Eq is 5x-4y+7z-70=0. Right? And any luck on the 2nd question?
13. ### Cartesian Eq. of Plane

That makes sense. Perhaps, they are the same? Just to be sure in the equation [x,y,z] = (-1,-2,-3) + s[5,-4,7], [5,-4,7] is the direction vector right? If that is the case, could we use Ax+By+Cz+D=0 and plug in 5 for A; -4 for B; 7 for C? And x,y,z would be 2, -1 and 8 respectively to solve...
14. ### Cartesian Eq. of Plane

Um I THINK they are parallel? Something in my head pops up about the normal being perpendicular to the line. So if the line is perpendicular to the plane, they are parallel? I'm likely wrong.
15. ### Cartesian Eq. of Plane

Homework Statement Write the Cartesian equation for the plane containing the point (2,-1,8) and perpendicular to the line [x,y,z] = [1,-2,-3] + s[5,-4,7]. The Attempt at a Solution The situation is that I have my Calc. + Vectors exam tomorrow morning and I'm just going through some...
16. ### Can't figure out next steps

You did a lot of unnecessary stuff there. Start on the left side. Cotangent (-x) is negative in the 4th quadrant, so what can that be expressed as? Cosine is positive in 4th quadrant so what can that be expressed as? Sine is negative in 4th quadrant, once again, adjust the sin(-x) into something...
17. ### Trigonometric Identities algebra

Yup, if the domain was [0,2pi], then it is correct.
18. ### Trigonometric Identities algebra

In your solution, you did not even mention pi/4. The double angle is as follows: 2cos^{2}x-1=0 cos2x=0 2x=pi/2 x=pi/4 That is only one solution, and you are still missing it. Check where you went wrong.
19. ### Trigonometric Identities algebra

Mspike, don't make that mistake. The cosx don't divide out. Since you have already pretty much attained your answer, this is what should have happened: \frac{2+2cosx}{sinx+sinxcosx} =\frac{2(1+cosx)}{sinx(1+cosx)} The (1+cosx) in the numerator and denominator divide out. =\frac{2}{sinx} =2cscx
20. ### Trigonometric Identities algebra

That should actually be \frac{sin^{2}x+1+2cosx+cos^{2}x}{sinx+sinxcosx} Simplify and then factor.
21. ### Finance Problems

Your final compounded value is incorrect. The answer is about $10475.76. Now that you have the compounded value, you can see that the interest you earn in that one year is$10475.76-7700=\$2775.76. I will leave it up to you to try the formula FV = PV (1+i)^n to find the answer that I got...
22. ### Trig Identity

Turn the denominator into \frac{cos(x)+1}{cos(x)}. So that would look like \frac{\frac{sin^{2}(x)}{cos(x)}}{\frac{cos(x)+1}{cos(x)}}. What icystrike showed is the faster way but since you're already this far, you can try what I suggested.
23. ### Fundamental Identities

The first step is to just divide the numerator on the left side by the denominator. Try it and you will see how it makes sense.
24. ### Find all solutions of the equation 3sin^2x-7sinx+2=0

Sorry, I didn't mean .34 pi. I just meant .34 rad. And as for the sin(30) = 2, likely no. That's why I said to him to not base his work on my steps. I was hoping someone would correct it and I'd learn something new. I just recall something about cot x = a. tan x = (1/a) x = tan- (1/a). I guess...
25. ### Find all solutions of the equation 3sin^2x-7sinx+2=0

You factored incorrectly. That should be (3sinx-1)(sinx-2)=0 So sin x = 1/3 and 2 Take the sine inverse of the two. Sin x = 2. csc 30 = 2 so sin- (1/2) = x. x=30 degrees or pi/6 rad. sin x = 1/3. sin- (1/3)=x. x=19.47 degrees or .34pi. That's what I would've done but I'm not sure if that...
26. ### Angular Velocity of a car

So basically you're just converting the units for speed and then dividing by the circumference of the tire, correct?
27. ### Angular Velocity of a car

Nevermind, I thought of it quite a bit and I think I've got the concept. But just to make sure: First 100 km/h is converted into 2777.78 cm/s. That is the speed at which the tire travels. So basically, every second, it moves 2777.78 cm. This would make it the arc length. Now we have to look...
28. ### Angular Velocity of a car

Homework Statement "A car is traveling at 100 km/h and the tire of the car has a radius of 36cm. Find the number of revolutions per second." The Attempt at a Solution 100 km/h * (10,000,000 cm/km) * (1h/3600 secs) = 2777.77777778 cm/s is the speed of the car. Θ = a/r Θ = (2777.78) / (36) Θ...
29. ### Trig Identies

Here are the two special triangles I've used in the past: http://fouss.pbworks.com/f/special%20triangle%203.JPG and http://fouss.pbworks.com/f/special%20triangle%202.JPG and recall that sin (a-b)=(sin a)(cos b)-(sin b)(cos a) Now sin \frac{-pi}{12} = sin (\frac{pi}{6} - \frac{pi}{4}) = sin...
30. ### Fractional Exponential

Nope, no mistakes. I'm in Pre-Calc at the moment too, none of this stuff so far. We worked on this kind of stuff in grade 11 if memory serves me right.
31. ### Equation of a parabola

y=2x2-2x+3 When you complete the square, you must factor out the leading co-efficient, which in this case is 2 from the terms with the variable. The 3 however will stay outside of the brackets. y=2(x2-x)+3 y=2(x2-x+0.25-0.25)+3 Bring out the negative 0.25 after multiplying it by the leading...
32. ### Jobs with Math + Physics?

Both, I suppose. I'm not sure if I NEED to take chemistry in high school to go into that field, and if I need to take it in my first two years also or not.
33. ### Jobs with Math + Physics?

Hmm. Thanks for the response. You mentioned that chemistry is only one course so all I need to do is pass it. But in the long run, don't the universities look at your marks over the four years, and not just the last? I'm talking about university marks, not high school. And do you need...
34. ### Jobs with Math + Physics?

Hello there! I'm almost halfway through grade 12 and I think it's time I finally chose the career path I wanted to pursue. I really like math and physics, but I'm horrible at chemistry and not sure about biology (dropped it in grade 11 because I needed to take another course for a social...
35. ### Prime Factorization Homework Problem 2

Look for their lowest common multiple. And that number is 12. 2000 + 12 = the year 2012
36. ### Prime Factorization Homework Problem 1

It can't be six weeks because Randa's appointment is every 4 weeks and that does not work. I didn't really bother doing any calculations but let's make a little table anyway. Margo has lessons every 2 weeks: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20 Boberto has soccer every 3 weeks: 3, 6, 9, 12...
37. ### Medical Surgery [Bankart Lesion] - I'm screwed

Oh boy. I really hope I don't end up having any restrictions on the motion. Especially at this age. And you're right, I'll try to get a second medical opinion this week from another doctor. Thanks.
38. ### Medical Surgery [Bankart Lesion] - I'm screwed

Thanks for the input guys. Yeah, I'm really scared about this. I mean I love sports and stuff and if this doesn't go well, I may be screwed for life. :S I likely will go for ANOTHER MRI and see if any healing occurred or not, even though the doctor said it wouldn't. Lisab, glad to hear your...
39. ### Medical Surgery [Bankart Lesion] - I'm screwed

So basically, I got a Bankart Lesion tear about half a year ago and I finally got the MRI results yesterday after repeating having my shoulder pull out of the socket while playing sports. Basically, repeatedly dislocations. The injury was to the Labrum. I've been resting it for about two months...
40. ### I face some difficulties to find the domain

As Bohrok said, if the domain was all real numbers for √(-1-s), it would be incorrect. Say s is equal to 2. -1-2 = -3. √-3 is an imaginary number. You want to make sure whatever is under the square root bracket is equal to 0 or more.
41. ### Simplifying Polynomials

But the numerator and denominator can be factored a bit more. Factor out the 4 in the numerator and the x in the denominator. You should get: 4(21x4y-13) / x(21x4y-13) The (21x4y-13) from the top and the bottom divide out and you are left with 4/x. The restrictions would be (21x4y-13) is not...
42. ### Math problem involving reciprocal of linear functions

Anytime! Good luck. :)
43. ### Math problem involving reciprocal of linear functions

t = distance / v distance = t * v distance = 11 * 350 distance = 3850 We know distance is 3850km since it takes 11 hours to reach from Quebec City to Montreal at a speed of 350km/h. Time is also inversely proportional to speed so that means as time goes up, speed goes down and vice-versa. t =...
44. ### Polynomial, Division, Remainder

@lanedance: I asked my teacher the same question and he gave the same answer as you. The degree of the remainder has to be one less than that of the divisor. Cheers! @:Hurkyl: I came across is while surfing Wikipedia but I have no practice with it at all.
45. ### Polynomial, Division, Remainder

Thanks for posting that. Just asking. You put g(0) in there, would it not be g(-2) and g(1) respectively? Just asking. Edit: Also, why was a linear equation (y=ax +b) of all options? Not sure about that.
46. ### Polynomial, Division, Remainder

If anyone was interested, here is how the answer is achieved. y = mx+b is the standard form for a linear equation So we divide the polynomial by a linear equation in the form (x-b) where b is equal to 1 (mx +b) / (x-1) = m with remainder m + b (mx+b) / (x+2) = m with remainder -2m + b We...
47. ### Polynomial, Division, Remainder

Thanks for the reply. And yeah, I didn't think I was doing it right either. I got as far as P(-2) = -19 and P(1) = 2. Not really sure where I need to go after that. The whole mess in the first post.. I was trying to make both sides equal, like one would do when solving for two...
48. ### Polynomial, Division, Remainder

Homework Statement When a polynomial is divided by (x+2), the remainder is -19. When the same polynomial is divided by (x-1), the remainder is 2. Determine the remainder when the polynomial is divided by (x+2)(x-1). EDIT: Took out my attempts lol, there were way off. This was a "Math...