1.3 Übungen
Aus Online Mathematik Brückenkurs 2
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Determine the critical points, the inflexion points, the local extrema and global extrema. Give also the intervals where the function is strictly increasing and strictly decreasing. | Determine the critical points, the inflexion points, the local extrema and global extrema. Give also the intervals where the function is strictly increasing and strictly decreasing. | ||
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</div>{{#NAVCONTENT:Answer|Answer 1.3:1|Solution a|Solution 1.3:1a|Solution b|Solution 1.3:1b|Solution c|Solution 1.3:1c|Solution d|Solution 1.3:1d}} | </div>{{#NAVCONTENT:Answer|Answer 1.3:1|Solution a|Solution 1.3:1a|Solution b|Solution 1.3:1b|Solution c|Solution 1.3:1c|Solution d|Solution 1.3:1d}} | ||
| - | === | + | ===Übung 1.3:2=== |
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Determine the local extrema and sketch the graph of | Determine the local extrema and sketch the graph of | ||
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</div>{{#NAVCONTENT:Answer|Answer 1.3:2|Solution a|Solution 1.3:2a|Solution b|Solution 1.3:2b|Solution c|Solution 1.3:2c|Solution d|Solution 1.3:2d}} | </div>{{#NAVCONTENT:Answer|Answer 1.3:2|Solution a|Solution 1.3:2a|Solution b|Solution 1.3:2b|Solution c|Solution 1.3:2c|Solution d|Solution 1.3:2d}} | ||
| - | === | + | ===Übung 1.3:3=== |
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Determine the local extrema and sketch the graph of | Determine the local extrema and sketch the graph of | ||
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</div>{{#NAVCONTENT:Answer|Answer 1.3:3|Solution a|Solution 1.3:3a|Solution b|Solution 1.3:3b|Solution c|Solution 1.3:3c|Solution d|Solution 1.3:3d|Solution e|Solution 1.3:3e}} | </div>{{#NAVCONTENT:Answer|Answer 1.3:3|Solution a|Solution 1.3:3a|Solution b|Solution 1.3:3b|Solution c|Solution 1.3:3c|Solution d|Solution 1.3:3d|Solution e|Solution 1.3:3e}} | ||
| - | === | + | ===Übung 1.3:4=== |
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</div>{{#NAVCONTENT:Answer|Answer 1.3:4|Solution|Solution 1.3:4}} | </div>{{#NAVCONTENT:Answer|Answer 1.3:4|Solution|Solution 1.3:4}} | ||
| - | === | + | ===Übung 1.3:5=== |
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</div>{{#NAVCONTENT:Answer|Answer 1.3:5|Solution|Solution 1.3:5}} | </div>{{#NAVCONTENT:Answer|Answer 1.3:5|Solution|Solution 1.3:5}} | ||
| - | === | + | ===Übung 1.3:6=== |
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A metal cup is to be made which has the form of a vertical circular cylinder. What radius and height should the cup have if it is to have a prescribed volume <math>V</math> as well as being made of as little metal as possible? | A metal cup is to be made which has the form of a vertical circular cylinder. What radius and height should the cup have if it is to have a prescribed volume <math>V</math> as well as being made of as little metal as possible? | ||
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</div>{{#NAVCONTENT:Answer|Answer 1.3:6|Solution|Solution 1.3:6}} | </div>{{#NAVCONTENT:Answer|Answer 1.3:6|Solution|Solution 1.3:6}} | ||
| - | === | + | ===Übung 1.3:7=== |
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A circular sector is cut out from a circular disc and the two radial edge which result are bound together to produce a cornet. What should the angle of the removed circular sector be so that the cornet has maximum volume? | A circular sector is cut out from a circular disc and the two radial edge which result are bound together to produce a cornet. What should the angle of the removed circular sector be so that the cornet has maximum volume? | ||
</div>{{#NAVCONTENT:Answer|Answer 1.3:7|Solution|Solution 1.3:7}} | </div>{{#NAVCONTENT:Answer|Answer 1.3:7|Solution|Solution 1.3:7}} | ||
Version vom 13:23, 10. Mär. 2009
| Theory | Übungen |
Übung 1.3:1
Determine the critical points, the inflexion points, the local extrema and global extrema. Give also the intervals where the function is strictly increasing and strictly decreasing.
| a) | 1.3 - Figure - The graph in exercise 1.3:1a | b) | 1.3 - Figure - The graph in exercise 1.3:1b |
| c) | 1.3 - Figure - The graph in exercise 1.3:1c | d) | 1.3 - Figure - The graph in exercise 1.3:1d |
Answer
Laden...
Solution a
Solution b
Solution c
Solution d
Übung 1.3:2
Determine the local extrema and sketch the graph of
| a) | \displaystyle f(x)= x^2 -2x+1 | b) | \displaystyle f(x)=2+3x-x^2 |
| c) | \displaystyle f(x)= 2x^3+3x^2-12x+1 | d) | \displaystyle f(x)=x^3-9x^2+30x-15 |
Answer
Solution a
Solution b
Solution c
Solution d
Übung 1.3:3
Determine the local extrema and sketch the graph of
| a) | \displaystyle f(x)=-x^4+8x^3-18x^2 | b) | \displaystyle f(x)=e^{-3x} +5x |
| c) | \displaystyle f(x)= x\ln x -9 | d) | \displaystyle f(x)=\displaystyle\frac{1+x^2}{1+x^4} |
| e) | \displaystyle f(x)=(x^2-x-1)e^x when \displaystyle -3\le x\le 3 |
Answer
Solution a
Solution b
Solution c
Solution d
Solution e
Übung 1.3:4
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Where, in the first quadrant, on the curve \displaystyle y=1-x^2 should the point \displaystyle P be chosen so that the rectangle in the figure to the right has maximum area? | 1.3 - Figure - The parabola y = 1 - x² with a rectangle |
Answer
Solution
Übung 1.3:5
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A 30 cm wide sheet of metal is to be used to make a channel. The edges are bent upwards parallel with the sheet's long sides, as shown in the figure. How large should the angle \displaystyle \alpha be so that the channel holds as much water as possible? | 1.3 - Figure - Channel |
Answer
Solution
Übung 1.3:6
A metal cup is to be made which has the form of a vertical circular cylinder. What radius and height should the cup have if it is to have a prescribed volume \displaystyle V as well as being made of as little metal as possible?
Answer
Solution
Übung 1.3:7
A circular sector is cut out from a circular disc and the two radial edge which result are bound together to produce a cornet. What should the angle of the removed circular sector be so that the cornet has maximum volume?
Answer
Solution
