Any short explanation for things I got wrong would be great, too, if possible! Thanks in advanced! :)
8. Which of the following functions grows the fastest?
***b(t)=t^4-3t+9
f(t)=2^t-t^3
h(t)=5^t+t^5
c(t)=sqrt(t^2-5t)
d(t)=(1.1)^t
9. Which of the following functions grows the fastest?
f(t)=2^t-t^3
a(t)=t^5/2
e(t)=e
g(t)=3t^2-t
***b(t)=t^4-3t+9
10. Which of the following functions grows the fastest?
***g(t)=3t^2-t
i(t)=1m(t^100)
e(t)=e
c(t)=sqrt(t^2-5t)
a(t)=t^5/2
11. Which of the following functions grows the slowest?
b(t)=t^4-3t+9
f(t)=2^t-t^3
h(t)=5^t+t^5
***c(t)=sqrt(t^2-5t)
d(t)=(1.1)^t
12. Which of the following functions grows the least?
g(t)=3t^2-t
i(t)=1n(t^100)
e(t)=e
c(t)=sqrt(t^2-5t)
***a(t)=t^5/2
13. Which of the following functions grows the slowest?
j(t)=1/4 1n(t^200)
a(t)=t^5/2
***i(t)=1n(t^100)
g(t)=3t^2-t
b(t)=t^4-3t+9
5 answers
logs grow even slower than roots (since exponentials grow faster than powers): log(x) < √x
So, in order of increasing growth rate, we have
#8: c,b,d,f,h
#9: e,g,a,b,f
#10: e,i,c,g,a
#11: c,b,d,f,h
#12: e,i,c,g,a
#13: j,a,i,g,b