Calculus and Above
Calculus Questions? Ask a Mathematician for Answers ASAP
Thank you for using the site, and thank you for requesting me.
Yes, I can be available at that time.
Ok, sounds good.
Thanks. I have seven image files for the first set.
Here are the solutions for the first set:
As always, please let me know if there are issues with any of these solutions.
Could you please send screenshots of what was entered?
For #1 and #3, there are different ways of entering what amounts to the same thing, so it's difficult to know what they expect.
For #14 and #15, there shouldn't be any issue with those as the problems were straightforward. I suspect that there is likely to be a typo issue there, so seeing what was entered might help.
For #1, change both from "1/5 + 1" to "6/5".
For #3, change both from "-6/5 + 1" to "-1/5".
For #14 and #15, add absolute value bars around the "x" in the natural logarithm terms.
Ok, got them.
Here are the solutions for the problems that were included in the images:
Note that problem #12 was not included in the screenshots, and problem #18 was cut off with no problem information shown.
Are those two separate problems?
Equation of the secant line through (-2, -6) and (4, 0) is y = x - 4.
The point c is (1, -12)
The equation of the tangent line through (1, -12), parallel to the secant line, is y = x - 13
Absolute minimum is -5/2
Absolute maximum is 40
C(6) = 12(1/6 + 6/9) = 12(5/6) = 10
C(3) = 12(1/3 + 3/6) = 12(5/6) = 10
Order size for minimum cost is 3/2 + (3√3)/2, or ≈ 4.098 (hundreds)
For F (x)=(x+7)^2/3:
Critical point at x = -7
Increasing on (-7, ∞)
Decreasing on (-∞, 7)
Maximum: No maximum
Rectangle with perimeter 7P:
Smaller value = 7P/4
Larger value = 7P/4
(The rectangle of "maximum area" is a square.)
Intercept = (0, 0)
Rel. Min. = -1/10, at x = -5
Rel. Max. = 1/10, at x = 5
Points of inflection = -5√3, 0, 5√3
Equation of asymptote: y = 0
Intercepts (there are 3 answer boxes): -4th root of 5, 0, +4th root of 5
Relative minimum: -4 at x = 1
Relative maximum: +4 at x = -1
Points of inflection: (0, 0)
Equation of asymptotes: No asymptotes
For the one about the package, what are X and Y? Is the end of the package square?
Ok. Is X the dimension of the square end, and Y the length?
If that is the case, then X = 12 inches and Y = 24 inches
For F (x)=x^5-5x?
The relative minimum is -4, and the relative maximum is 4.
Those are also the absolute minimum and maximum.
Critical value: x = 1
G (x)=2 (x-1)G (0)=2 (0 -1)G (0)=2 (-1 )G (0)=-2
G (x)=2 (x-1)G (2)=2 (2 -1)G (2)=2 (1 )G (2)=2
Intercepts: -6th root of 7, 0, +6th root of 7
Relative minimum: -6
Relative maximum: +6
Inflection point is (0, 0)
y'(x) = 42x^5
Is the second part really asking when "y" is equal to 0, or is is "y-prime"?
Ok, great. I wasn't sure what they wanted for "c" there. It could have been just the x-coordinate, or it could have been the (x, y) ordered pair.
I have the first 8 screenshots for Set 3. Please let me know if there are more, and when the deadline is for completion.
Could you please post a screenshot of "Example 1"? It is referred to in problem #1, and I'm concerned that the "correct" answer might be slightly different than just calculating the straight integral.
Here are the remaining solutions:
Please let me know if there are any issues.
Ok, thanks for the update.