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Math Problems
Calculus
Find limits of polynomials and rational functions
Condense the logarithm. Assume all expressions exist and are well-defined.
\newline
log
2
9
−
log
2
4
\log_2 9 - \log_2 4
lo
g
2
9
−
lo
g
2
4
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Condense the logarithm. Assume all expressions exist and are well-defined.
\newline
log
a
5
+
log
a
3
\log_a 5 + \log_a 3
lo
g
a
5
+
lo
g
a
3
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lim
x
→
∞
2
x
4
−
7
4
x
8
+
7
x
5
\lim _{x\to \infty }\frac{2x^4-7}{\sqrt{4x^8+7x^5}}
x
→
∞
lim
4
x
8
+
7
x
5
2
x
4
−
7
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Give an example of a
2
×
2
2 \times 2
2
×
2
matrix, then calculate its determinant using elementary row operations!
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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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lim
x
→
−
5
x
2
+
5
x
x
2
+
2
x
−
15
\lim _{x \rightarrow-5} \frac{x^{2}+5 x}{x^{2}+2 x-15}
lim
x
→
−
5
x
2
+
2
x
−
15
x
2
+
5
x
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What's the limit of
(
2
x
+
3
x
)
\left(\frac{2x + 3}{x}\right)
(
x
2
x
+
3
)
when
x
x
x
tends to infinity?
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Integrate
1
1
+
x
2
\frac{1}{1+x^{2}}
1
+
x
2
1
for limit
[
0
,
1
]
[0,1]
[
0
,
1
]
.
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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
→
∞
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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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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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.
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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
+
1
x
2
+
1
\lim _{x \rightarrow \infty} \frac{x+1}{x^{2}+1}
lim
x
→
∞
x
2
+
1
x
+
1
.
\newline
Choose
1
1
1
answer:
\newline
(A)
1
1
1
\newline
(B)
2
2
2
\newline
(C)
0
0
0
\newline
(D) The limit is unbounded
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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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