36: Find the limit: lim, x -> 0, (sin 4x)/(sin 6x)

I'm pretty sure I need to use the fact that lim, x->0, (sin x)/(x) = 1 (they gave us that in the section), but I don't see how...?

Thanks in advance

36: Find the limit: lim, x -> 0, (sin 4x)/(sin 6x)

I'm pretty sure I need to use the fact that lim, x->0, (sin x)/(x) = 1 (they gave us that in the section), but I don't see how...?

Thanks in advance

I'm pretty sure I need to use the fact that lim, x->0, (sin x)/(x) = 1 (they gave us that in the section), but I don't see how...?

Thanks in advance

- on Sun Dec 14, 2008 11:24 pm
- Forum: Calculus
- Topic: find limit of (sin 4x) / (sin 6x) as x goes to zero
- Replies:
**2** - Views:
**8419**

Thanks for the warning!

- on Mon Dec 15, 2008 1:51 pm
- Forum: Calculus
- Topic: find limit of (sin 4x) / (sin 6x) as x goes to zero
- Replies:
**2** - Views:
**8419**

This is from my calculus book, but I think I only need algebra: Find the constant c that makes g continuous on (-infinity, +infinity): . / | x^2 - c^2 if x < 4 g(x) = < | cx + 20 if x >= 4 \ (The dot above doesn't mean anything, but the first line wouldn't line up without a leading character...

- on Mon Dec 15, 2008 2:01 pm
- Forum: Advanced Algebra ("pre-calculus")
- Topic: find the constant c that makes g continuous (g in two parts)
- Replies:
**1** - Views:
**6240**

Prove that the function f(x) = x^101 + x^51 + x + 1 has neither a local maximum nor a local minimum.

I can take the derivative: f'(x) = 101x^100 + 51x^50 + 1

But what then?

I can take the derivative: f'(x) = 101x^100 + 51x^50 + 1

But what then?

- on Thu Jan 22, 2009 5:29 pm
- Forum: Calculus
- Topic: Prove f(x) = x^101 + x^51 + x + 1 has no local max/min
- Replies:
**3** - Views:
**5412**

The quadratic formula gives me x^50 = (-51+/-sqrt[(-51)^2-4(101)])/(2*101) = (-51+/-sqrt[2197])/(202) = (-51+/-46.9)/(202). The -51+/-46.9 will always be negative, so I can't do the 50th root of it to get a number for x. So this means I can't get a zero, so there isn't a critical point, so there can...

- on Mon Jan 26, 2009 1:08 pm
- Forum: Calculus
- Topic: Prove f(x) = x^101 + x^51 + x + 1 has no local max/min
- Replies:
**3** - Views:
**5412**

Use the Mean Value Theorem to prove the inequality |sin(a) - sin(b)| <= |a - b| for all a and b.

The MVT says that there is some c between a and b so sin(a) - sin(b) = cos(c)(a - b). Where do I go from there?

The MVT says that there is some c between a and b so sin(a) - sin(b) = cos(c)(a - b). Where do I go from there?

- on Mon Jan 26, 2009 1:16 pm
- Forum: Calculus
- Topic: Use Mean Value Theorem to show |sin(a)-sin(b)|<=|a-b|
- Replies:
**1** - Views:
**5730**

For what values of the numbers a and b does the function f(x)\, =\, axe^{bx^2} have the maximum value f(2)\, =\, 1 \mbox{?} f(2)\, =\, a(2)e^{b(2)^2}\, =\, 2ae^{4b}\, =\, 1 We've done the derivative tests. f'(x)\, =\, ae^{bx^2}\, +\, ax\left(2b...

- on Fri Jan 30, 2009 2:30 am
- Forum: Calculus
- Topic: values where f(x) = axe^(bx^2) has max f(2) = 1
- Replies:
**1** - Views:
**8489**

Find the points on the ellipse 4x^{2} + y^{2} = 4 that are farthest away from the point (1, 0).

I must be forgetting something easy, to get started.

I must be forgetting something easy, to get started.

- on Fri Feb 06, 2009 7:54 pm
- Forum: Calculus
- Topic: find points on ellipse 4x^2 + y^2 = 4 furthest from (1, 0)
- Replies:
**3** - Views:
**8538**

So I get a "distance" function of d(x)\, =\, 5\, -\, 2x\, -\, 3x^2 . The max/min points are the critical points, so d'(x)\, =\, -2\, -\, 6x\, =\, 0 , or x = -1/3. For x = 3, I get 4\left(-\frac{1}{3}\right)^2\, +\, y^2\, = 4 , so y\, =\, \pm \frac{4\sqrt{2}}{3} ...

- on Mon Feb 09, 2009 2:41 pm
- Forum: Calculus
- Topic: find points on ellipse 4x^2 + y^2 = 4 furthest from (1, 0)
- Replies:
**3** - Views:
**8538**

The upper right-hand corner of a piece of paper, 12 inches long by 8 inches high, is folded over to the bottom edge. How would you fold it so as to minimize the length of the fold? There is a right triangle folded down from the right-hand corner. The picture shows "x" as the amount folded...

- on Mon Feb 16, 2009 6:52 pm
- Forum: Calculus
- Topic: minimizing length of fold in sheet of paper
- Replies:
**2** - Views:
**4299**