Processing Math: Done
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 (-Övningar +Exercises))
K (Robot: Automated text replacement (-Svar +Answer))
Zeile 26: Zeile 26:
||{{:1.1 - Figur - Grafen till f(x) i övning 1.1:1}}
||{{:1.1 - Figur - Grafen till f(x) i övning 1.1:1}}
|}
|}
-
</div>{{#NAVCONTENT:Answer|Svar 1.1:1|Solution a|Lösning 1.1:1a|Solution b|Lösning 1.1:1b|Solution c|Lösning 1.1:1c}}
+
</div>{{#NAVCONTENT:Answer|Answer 1.1:1|Solution a|Lösning 1.1:1a|Solution b|Lösning 1.1:1b|Solution c|Lösning 1.1:1c}}
===Exercise 1.1:2===
===Exercise 1.1:2===
Zeile 46: Zeile 46:
|width="33%"| <math>f(x)= \cos (x+\pi/3)</math>
|width="33%"| <math>f(x)= \cos (x+\pi/3)</math>
|}
|}
-
</div>{{#NAVCONTENT:Answer|Svar 1.1:2|Solution a|Lösning 1.1:2a|Solution b|Lösning 1.1:2b|Solution c|Lösning 1.1:2c|Solution d|Lösning 1.1:2d|Solution e|Lösning 1.1:2e|Solution f|Lösning 1.1:2f}}
+
</div>{{#NAVCONTENT:Answer|Answer 1.1:2|Solution a|Lösning 1.1:2a|Solution b|Lösning 1.1:2b|Solution c|Lösning 1.1:2c|Solution d|Lösning 1.1:2d|Solution e|Lösning 1.1:2e|Solution f|Lösning 1.1:2f}}
===Exercise 1.1:3===
===Exercise 1.1:3===
Zeile 52: Zeile 52:
A small ball, that is released from a height of <math>h=10</math>m above the ground at time <math>t=0</math>, is at a height <math>h(t)=10-\displaystyle\frac{9{,}82}{2}\,t^2</math> at time <math>t</math> (measured in seconds) What is the speed of the ball when it hits the grounds?
A small ball, that is released from a height of <math>h=10</math>m above the ground at time <math>t=0</math>, is at a height <math>h(t)=10-\displaystyle\frac{9{,}82}{2}\,t^2</math> at time <math>t</math> (measured in seconds) What is the speed of the ball when it hits the grounds?
-
</div>{{#NAVCONTENT:Answer|Svar 1.1:3|Solution |Lösning 1.1:3}}
+
</div>{{#NAVCONTENT:Answer|Answer 1.1:3|Solution |Lösning 1.1:3}}
===Exercise 1.1:4===
===Exercise 1.1:4===
Zeile 58: Zeile 58:
Determine the equation for the tangent and normal to the curve <math>y=x^2</math> at the point <math>(1,1)</math>.
Determine the equation for the tangent and normal to the curve <math>y=x^2</math> at the point <math>(1,1)</math>.
-
</div>{{#NAVCONTENT:Answer|Svar 1.1:4|Solution |Lösning 1.1:4}}
+
</div>{{#NAVCONTENT:Answer|Answer 1.1:4|Solution |Lösning 1.1:4}}
===Exercise 1.1:5===
===Exercise 1.1:5===
Zeile 64: Zeile 64:
Determine all the points on the curve <math>y=-x^2</math> which have a tangent that goes through the point <math>(1,1)</math>.
Determine all the points on the curve <math>y=-x^2</math> which have a tangent that goes through the point <math>(1,1)</math>.
-
</div>{{#NAVCONTENT:Answer|Svar 1.1:5|Solution |Lösning 1.1:5}}
+
</div>{{#NAVCONTENT:Answer|Answer 1.1:5|Solution |Lösning 1.1:5}}

Version vom 14:12, 16. Sep. 2008

 
  1. REDIRECT Template:Nicht gewählter Tab
  2. REDIRECT Template:Gewählter Tab
 

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 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 y=x2 at the point (11).

Answer | Solution

Exercise 1.1:5

Determine all the points on the curve y=−x2 which have a tangent that goes through the point (11).

Answer | Solution

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