no ideas on any of these?
#1 as x gets huge, f(x) just looks like x^4/x^3
#2 as x gets huge, exponentials outpace any polynomial, so f(x) just looks like 2^x/3^x = (2/3)^x
#3 as x->0, you have 9/0
#4 II only
#5 cot(pi) = 1/tan(pi)
#6 use L'Hospital's Rule to get -sin(x)/1
#7 no trick at all
#8 exponentials outpace polynomials
larger base grows faster
#9 ditto
#10 ditto (I think - here there be typos?)
#11 powers are slower than exponentials.
lower powers are slower than higher powers
#12 logs are even slower than roots
#13 ditto
1. Evaluate:
lim x->infinity(x^4-7x+9)/(4+5x+x^3)
0
1/4
1
4
The limit does not exist.
2. Evaluate:
lim x->infinity (2^x+x^3)/(x^2+3^x)
0
1
3/2
2/3
The limit does not exist.
3. lim x->0 (x^3-7x+9)/(4^x+x^3)
0
1/4
1
9
The limit does not exist.
4.For the function g(f)=4f^4-4^f, which of the following statements are true?
I. lim f->0 g(f)=-1
II. lim f->infinity g(f)=-infinity
III. g(f) has 2 roots.
I only
II only
III only
I and II only
I, II, and III
5. lim cot(3x)
x->pi/3
sqrt3
1
(sqrt3)/3
0
The limit does not exist.
6. lim (cos(x)-1)/(x)
x->0
1
0
(sqrt2)/(2)
-1
The limit does not exist.
7. lim cos(x)-x
x->0
1
0
(sqrt3)/(2)
1/2
The limit does not exist.
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
1 answer