Mathe 1.)
1a.)Define the maximum of the definition set of the functions f and g.
Explain what kind of discontinuity can be found: Poles or removable discontinuity?
b.) Investigate if there are any asymptotes with regards to the functions g and f, name the linear equation.
c.) Define the extreme points of the functions g and f with the help of the second derivation.
2a.) A car is loosing 20% of its value during 1 year. At what time will the car be only worth one quarter of its purchase price?
b.) A flower grows so fast that it doubled in size in 15 years. How much percent does the flower grow per year?
c.) The radioactive decay of a substance with a half-life of 8 hours follows the function of decay….
x= the time in hours
k= decay constant
f(x)= the amount of mass remaining after the time x of the substance in milligramm
Define:
– the amount of the beginning of the substance
– k
– the amount of the substance after 3 days
3.)Perform a complete investigation of the function f:x->2x²*2-x
Mathe 2.)
1a.) Define the following integrals.
2a.) Calculate the surface area, which is surrounded by the graph with the x-axis.
3a.) Calculate the surface area, which is surrounded the graphs of the functions f and g. Have a look at the “finite areas”.
4a.) Show that both the tangents at x=-2 and x=2 intersect at one point the x-axis.
b.) Calculate the area, which the parabola of task a.) is surrounding.
5a.) Show that the functions fk are symmetrical.
b.) Define the point zero of fk in dependance of k.
c.) Draw the graph for k=2
d.) For which k is the content of the area,which the graph fk includes in the x-axis, consisting of only 12 unites of area?
7a.) Calculate the inproper integral
b.) If the function f rotates around the x-axis, then a body of rotation arises with an infinite volume. Calculate this volume in the intervall…….