Processing Math: 76%
To print higher-resolution math symbols, click the
Hi-Res Fonts for Printing button on the jsMath control panel.
No jsMath TeX fonts found -- using image fonts instead.
These may be slow and might not print well.
Use the jsMath control panel to get additional information.
jsMath Control PanelHide this Message

jsMath

1.1 Übungen

Aus Online Mathematik Brückenkurs 2

(Unterschied zwischen Versionen)
Wechseln zu: Navigation, Suche
K (Robot: Automated text replacement (-{{Ej vald flik +{{Not selected tab))
K (Robot: Automated text replacement (-{{Vald flik +{{Selected tab))
Zeile 3: Zeile 3:
| style="border-bottom:1px solid #000" width="5px" |  
| style="border-bottom:1px solid #000" width="5px" |  
{{Not selected tab|[[1.1 Introduction to derivatives|Theory]]}}
{{Not selected tab|[[1.1 Introduction to derivatives|Theory]]}}
-
{{Vald flik|[[1.1 Exercises|Exercises]]}}
+
{{Selected tab|[[1.1 Exercises|Exercises]]}}
| style="border-bottom:1px solid #000" width="100%"|  
| style="border-bottom:1px solid #000" width="100%"|  
|}
|}

Version vom 08:19, 17. Sep. 2008

       Theory          Exercises      

Exercise 1.1:1

The graph for f(x) is shown in the figure.

a) What are the signs of f(−4) and f(1)?
b) For what values of x is f(x)=0?
c) In which interval(s) is f(x) negative?

(Each square in the grid of the figure has width and height 1.)

1.1 - Figur - Grafen till f(x) i övning 1.1:1

Answer | Solution a | Solution b | Solution c

Exercise 1.1:2

Determine the derivative f(x) when

a) f(x)=x2−3x+1 b) f(x)=cosx−sinx c) f(x)=ex−lnx
d) f(x)=x  e) f(x)=(x2−1)2 f) f(x)=cos(x+3)

Answer | Solution a | Solution b | Solution c | Solution d | Solution e | Solution f

Exercise 1.1:3

A small ball, that is released from a height of h=10m above the ground at time t=0, is at a height h(t)=10−2982t2 at time \displaystyle t (measured in seconds) What is the speed of the ball when it hits the grounds?

Answer | Solution

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).

Answer | Solution

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).

Answer | Solution

Von „http://wiki.math.se/wikis/2009/bridgecourse2-TU-Berlin/index.php/1.1_%C3%9Cbungen“