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Math Problems
Precalculus
Find limits of polynomials and rational functions
Find
lim
h
→
0
5
arcsin
(
2
3
+
h
)
−
5
arcsin
(
2
3
)
h
\lim _{h \rightarrow 0} \frac{5 \arcsin \left(\frac{2}{3}+h\right)-5 \arcsin \left(\frac{2}{3}\right)}{h}
lim
h
→
0
h
5
a
r
c
s
i
n
(
3
2
+
h
)
−
5
a
r
c
s
i
n
(
3
2
)
.
\newline
Choose
1
1
1
answer:
\newline
(A)
3
5
3 \sqrt{5}
3
5
\newline
(B)
5
3
\frac{\sqrt{5}}{3}
3
5
\newline
(C)
3
5
5
\frac{3 \sqrt{5}}{5}
5
3
5
\newline
(D) The limit doesn't exist
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What happens to the value of the expression
3
e
3e
3
e
as
e
e
e
increases?
\newline
Choose
1
1
1
answer:
\newline
(A) It increases.
\newline
(B) It decreases.
\newline
(C) It stays the same.
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Find
lim
x
→
−
4
7
x
+
28
x
2
+
x
−
12
\lim_{x \to -4}\frac{7x+28}{x^{2}+x-12}
lim
x
→
−
4
x
2
+
x
−
12
7
x
+
28
\newline
Choose
1
1
1
answer:
\newline
(A)
1
1
1
\newline
(B)
7
7
7
\newline
(C)
−
1
-1
−
1
\newline
(D) The limit doesn't exist
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Determine the following limit in simplest form. If the limit is infinite, state that the limit does not exist (DNE).
\newline
lim
x
→
∞
−
19
x
3
+
36
x
4
3
+
x
+
x
2
\lim _{x \rightarrow \infty} \frac{\sqrt{-19 x^{3}+36 x^{4}}}{3+x+x^{2}}
x
→
∞
lim
3
+
x
+
x
2
−
19
x
3
+
36
x
4
\newline
Answer:
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Determine the following limit in simplest form. If the limit is infinite, state that the limit does not exist (DNE).
\newline
lim
x
→
∞
23
x
+
64
x
9
7
x
4
+
6
x
3
\lim _{x \rightarrow \infty} \frac{\sqrt{23 x+64 x^{9}}}{7 x^{4}+6 x^{3}}
x
→
∞
lim
7
x
4
+
6
x
3
23
x
+
64
x
9
\newline
Answer:
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Determine the following limit in simplest form. If the limit is infinite, state that the limit does not exist (DNE).
\newline
lim
x
→
∞
25
x
4
−
28
x
2
3
x
+
5
x
2
\lim _{x \rightarrow \infty} \frac{\sqrt{25 x^{4}-28 x^{2}}}{3 x+5 x^{2}}
x
→
∞
lim
3
x
+
5
x
2
25
x
4
−
28
x
2
\newline
Answer:
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What happens to the value of the expression
3
y
2
y
\frac{3y}{2y}
2
y
3
y
as
y
y
y
increases?
\newline
Choose
1
1
1
answer:
\newline
(A) It increases.
\newline
(B) It decreases.
\newline
(C) It stays the same.
Get tutor help
Find
lim
x
→
4
3
x
(
x
−
2
)
(
x
+
2
)
\lim _{x \rightarrow 4} \frac{3 x}{(x-2)(x+2)}
lim
x
→
4
(
x
−
2
)
(
x
+
2
)
3
x
.
\newline
Choose
1
1
1
answer:
\newline
(A)
1
4
\frac{1}{4}
4
1
\newline
(B)
3
4
\frac{3}{4}
4
3
\newline
(C)
1
1
1
\newline
(D) The limit doesn't exist
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Find
lim
x
→
∞
x
2
−
4
x
+
4
\lim _{x \rightarrow \infty} \frac{x^{2}-4}{x+4}
lim
x
→
∞
x
+
4
x
2
−
4
.
\newline
Choose
1
1
1
answer:
\newline
(A)
1
1
1
\newline
(B)
−
1
-1
−
1
\newline
(C)
0
0
0
\newline
(D) The limit is unbounded
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