1.1 Övningar
Aus Förberedande kurs i matematik 2
(Unterschied zwischen Versionen)
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| - | |width="100%"| For what values of <math>x</math> | + | |width="100%"| For what values of <math>x</math> is <math>f^{\,\prime}(x)=0</math>? |
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| valign="top" |c) | | valign="top" |c) | ||
| - | |width="100%"| In which interval(s) is<math>f^{\,\prime}(x)</math> negative? | + | |width="100%"| In which interval(s) is <math>f^{\,\prime}(x)</math> negative? |
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(Each square in the grid of the figure has width and height 1.) | (Each square in the grid of the figure has width and height 1.) | ||
Aktuelle Version
| Theory | exercises |
exercise 1.1:1
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The graph for \displaystyle f(x) is shown in the figure.
(Each square in the grid of the figure has width and height 1.) |
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![[Image]](/wikis/2008/bridgecourse2-TU-Berlin/img_auth.php/metapost/6/a/2/6a260dcf937e32a9315ffb6cf330d510.png)
Laden...exercise 1.1:2
Determine the derivative \displaystyle f^{\,\prime}(x) when
| a) | \displaystyle f(x) = x^2 -3x +1 | b) | \displaystyle f(x)=\cos x -\sin x | c) | \displaystyle f(x)= e^x-\ln x |
| d) | \displaystyle f(x)=\sqrt{x} | e) | \displaystyle f(x) = (x^2-1)^2 | f) | \displaystyle f(x)= \cos (x+\pi/3) |
Svar
Lösning a
Lösning b
Lösning c
Lösning d
Lösning e
Lösning f
exercise 1.1:3
A small ball, that is released from a height of \displaystyle h=10m above the ground at time \displaystyle t=0, is at a height \displaystyle h(t)=10-\displaystyle\frac{9{,}82}{2}\,t^2 at time \displaystyle t (measured in seconds) What is the speed of the ball when it hits the grounds?
Svar
Lösning
exercise 1.1:4
Determine the equation for the tangent and normal to the curve \displaystyle y=x^2 at the point \displaystyle (1,1).
Svar
Lösning
exercise 1.1:5
Determine all the points on the curve \displaystyle y=-x^2 which have a tangent that goes through the point \displaystyle (1,1).
Svar
Lösning
