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suluclac
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Yesterday,
11:54
MarkFL
replied to a thread
Differentiation challenge
in
Challenge Questions and Puzzles
We appreciate challenge problems of virtually any level of difficulty. My advice to everyone is that if you find a posted problem "too easy" to...
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7 replies | 153 view(s)
January 19th, 2017,
10:19
MarkFL
replied to a thread
Minimum of function under constraint
in
Calculus
Yes, the function as a whole is not bounded from below or from above. Let's look at this using Lagrange Multipliers... We have the objective...
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6 replies | 81 view(s)
January 18th, 2017,
22:47
MarkFL
replied to a thread
Minimum of function under constraint
in
Calculus
You also need to check the boundaries of the function, one of which is $x=0$, at which the function is discontinuous. Another way to find the range...
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6 replies | 81 view(s)
January 18th, 2017,
20:13
MarkFL
replied to a thread
Minimum of function under constraint
in
Calculus
The function: f(x)=\frac{36}{x}+x has 2 local extrema, but we need to also look at the range, which is $(-\infty,-6]\,\cup\,[6,\infty)$. You...
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6 replies | 81 view(s)
January 17th, 2017,
17:35
MarkFL
replied to a thread [SOLVED]
231.12.3.63 Determine the smallest distance between point P and the line L through the origin
in
Calculus
The square of the distance is: D^2=(x+8)^2+(6x-4)^2=37x^2-32x+80 Critical value is from: 74x-32=0\implies x=\frac{16}{37} ...
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2 replies | 60 view(s)
January 16th, 2017,
19:00
greg1313
replied to a thread [SOLVED]
231.12.3.19 angle between vectors
in
Calculus
Your answer looks good to me. What are the zeros for? Cross-product is 3-d. What you have here appears to be 2-d and you've used the dot product.
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3 replies | 67 view(s)
January 16th, 2017,
18:23
greg1313
replied to a thread
Parabola question
in
Pre-Algebra and Algebra
That's correct. Alternatively, we have $$b=5(a)^2+a(a)+b\implies a=0$$ Substituting $-\frac{a}{10}=0$ for $x$ into $y=5x^2+ax+b$ gives...
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5 replies | 97 view(s)
January 16th, 2017,
17:17
MarkFL
replied to a thread
Parabola question
in
Pre-Algebra and Algebra
Yes, that's what I got too. (Yes) So then, what is $y_{\min}$?
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5 replies | 97 view(s)
January 16th, 2017,
16:04
MarkFL
replied to a thread
Parabola question
in
Pre-Algebra and Algebra
We know the axis of symmetry for the general quadratic: f(x)=ax^2+bx+c is the line: x=-\frac{b}{2a} And so for the given function:
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5 replies | 97 view(s)
January 15th, 2017,
15:39
greg1313
replied to a thread
Smilie Tabs: Easier Access To Smilies
in
Announcements
Cool. :cool:(Cool)(Malthe) Thanks MarkFL and MHB!
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3 replies | 110 view(s)
January 15th, 2017,
15:03
MarkFL
started a thread
Smilie Tabs: Easier Access To Smilies
in
Announcements
Hello MHB Community! (Wave) We have just installed a new feature that will make adding smilies to your posts easier and more efficient. When you...
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3 replies | 110 view(s)
January 15th, 2017,
10:59
MarkFL
replied to a thread
Prove that sin(x)+cos(x) is equal or larger than 1
in
Trigonometry
We could use Lagrange Multipliers...consider the objective function: f(x,y)=\sin(x)-\sin(y) Subject to the constraint: ...
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11 replies | 287 view(s)
January 15th, 2017,
09:39
greg1313
replied to a thread
Prove that sin(x)+cos(x) is equal or larger than 1
in
Trigonometry
Yes; quite right. My apologies for my blunder. :o
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11 replies | 287 view(s)
January 14th, 2017,
21:29
greg1313
replied to a thread [SOLVED]
206.08.05.44 partial fraction decomposition
in
Calculus
Differentiate $3/u$. What is $\frac{\sin(\theta)\cos(\theta)}{2}+\frac{\theta}{2}$ in terms of $x$?
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6 replies | 150 view(s)
January 14th, 2017,
17:13
greg1313
replied to a thread [SOLVED]
206.08.05.44 partial fraction decomposition
in
Calculus
First one's ok. You've made a sign error on the second one and haven't completed the back-sub. For the third, you should be integrating with respect...
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6 replies | 150 view(s)
January 14th, 2017,
13:40
greg1313
replied to a thread
Prove that sin(x)+cos(x) is equal or larger than 1
in
Trigonometry
Your proof is ok, it's your conclusion that needs work. See vidyarth's post (post #2). As an alternative, write $\sin(x)-\cos(x)$ as...
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11 replies | 287 view(s)
January 13th, 2017,
03:57
greg1313
replied to a thread
Prove that sin(x)+cos(x) is equal or larger than 1
in
Trigonometry
Your conclusion only shows that the original statement must be true at $x=\frac{\pi}{2}$. What about the remainder of the interval? Does your...
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11 replies | 287 view(s)
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