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Math Problems
Calculus
Find derivatives of logarithmic functions
lim
x
→
0
tan
(
x
)
=
?
\lim _{x \rightarrow 0} \tan (x)=?
x
→
0
lim
tan
(
x
)
=
?
\newline
Choose
1
1
1
answer:
\newline
(A)
−
1
-1
−
1
\newline
(B)
0
0
0
\newline
(C)
1
1
1
\newline
(D) The limit doesn't exist.
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lim
x
→
π
6
cot
(
x
)
=
?
\lim _{x \rightarrow \frac{\pi}{6}} \cot (x)=?
x
→
6
π
lim
cot
(
x
)
=
?
\newline
Choose
1
1
1
answer:
\newline
(A)
3
3
\frac{\sqrt{3}}{3}
3
3
\newline
(B)
3
2
\frac{\sqrt{3}}{2}
2
3
\newline
(C)
3
\sqrt{3}
3
\newline
(D) The limit doesn't exist.
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lim
x
→
π
cot
(
x
)
=
?
\lim _{x \rightarrow \pi} \cot (x)=?
x
→
π
lim
cot
(
x
)
=
?
\newline
Choose
1
1
1
answer:
\newline
(A)
−
1
-1
−
1
\newline
(B)
0
0
0
\newline
(C)
1
1
1
\newline
(D) The limit doesn't exist.
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lim
x
→
π
2
sin
(
x
)
=
?
\lim _{x \rightarrow \frac{\pi}{2}} \sin (x)=?
x
→
2
π
lim
sin
(
x
)
=
?
\newline
Choose
1
1
1
answer:
\newline
(A)
−
1
-1
−
1
\newline
(B)
0
0
0
\newline
(C)
1
1
1
\newline
(D) The limit doesn't exist.
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lim
x
→
0
cos
(
x
)
=
?
\lim _{x \rightarrow 0} \cos (x)=?
x
→
0
lim
cos
(
x
)
=
?
\newline
Choose
1
1
1
answer:
\newline
(A)
−
1
-1
−
1
\newline
(B)
0
0
0
\newline
(C)
1
1
1
\newline
(D) The limit doesn't exist.
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lim
x
→
0
csc
(
x
)
=
?
\lim _{x \rightarrow 0} \csc (x)=?
x
→
0
lim
csc
(
x
)
=
?
\newline
Choose
1
1
1
answer:
\newline
(A)
−
1
-1
−
1
\newline
(B)
0
0
0
\newline
(C)
1
1
1
\newline
(D) The limit doesn't exist.
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lim
x
→
π
cos
(
x
)
=
?
\lim _{x \rightarrow \pi} \cos (x)=?
x
→
π
lim
cos
(
x
)
=
?
\newline
Choose
1
1
1
answer:
\newline
(A)
−
1
-1
−
1
\newline
(B)
0
0
0
\newline
(C)
1
1
1
\newline
(D) The limit doesn't exist.
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lim
x
→
π
tan
(
x
)
=
?
\lim _{x \rightarrow \pi} \tan (x)=?
x
→
π
lim
tan
(
x
)
=
?
\newline
Choose
1
1
1
answer:
\newline
(A)
−
1
-1
−
1
\newline
(B)
0
0
0
\newline
(C)
1
1
1
\newline
(D) The limit doesn't exist.
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g
(
x
)
=
{
2
x
−
1
for
−
8
≤
x
<
1
x
for
x
≥
1
g(x)=\left\{\begin{array}{ll} 2^{x}-1 & \text { for }-8 \leq x<1 \\ \sqrt{x} & \text { for } x \geq 1 \end{array}\right.
g
(
x
)
=
{
2
x
−
1
x
for
−
8
≤
x
<
1
for
x
≥
1
\newline
Find
lim
x
→
4
g
(
x
)
\lim _{x \rightarrow 4} g(x)
lim
x
→
4
g
(
x
)
.
\newline
Choose
1
1
1
answer:
\newline
(A)
1
1
1
\newline
(B)
2
2
2
\newline
(C)
15
15
15
\newline
(D) The limit doesn't exist.
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h
(
x
)
=
{
5
x
for
x
<
−
2
x
3
−
2
for
x
≥
−
2
h(x)=\left\{\begin{array}{ll} 5 x & \text { for } x<-2 \\ x^{3}-2 & \text { for } x \geq-2 \end{array}\right.
h
(
x
)
=
{
5
x
x
3
−
2
for
x
<
−
2
for
x
≥
−
2
\newline
Find
lim
x
→
−
2
h
(
x
)
\lim _{x \rightarrow-2} h(x)
lim
x
→
−
2
h
(
x
)
.
\newline
Choose
1
1
1
answer:
\newline
(A)
−
10
-10
−
10
\newline
(B)
−
2
-2
−
2
\newline
(C)
10
10
10
\newline
(D) The limit doesn't exist.
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lim
x
→
π
4
cot
(
x
)
=
?
\lim _{x \rightarrow \frac{\pi}{4}} \cot (x)=?
x
→
4
π
lim
cot
(
x
)
=
?
\newline
Choose
1
1
1
answer:
\newline
(A)
2
2
\frac{\sqrt{2}}{2}
2
2
\newline
(B)
1
1
1
\newline
(C)
2
\sqrt{2}
2
\newline
(D) The limit doesn't exist.
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f
(
x
)
=
{
sin
(
x
)
for
0
≤
x
≤
π
x
π
−
1
for
π
<
x
≤
10
f(x)=\left\{\begin{array}{ll} \sin (x) & \text { for } 0 \leq x \leq \pi \\ \frac{x}{\pi}-1 & \text { for } \pi<x \leq 10 \end{array}\right.
f
(
x
)
=
{
sin
(
x
)
π
x
−
1
for
0
≤
x
≤
π
for
π
<
x
≤
10
\newline
Find
lim
x
→
π
f
(
x
)
\lim _{x \rightarrow \pi} f(x)
lim
x
→
π
f
(
x
)
.
\newline
Choose
1
1
1
answer:
\newline
(A)
−
1
-1
−
1
\newline
(B)
0
0
0
\newline
(C)
π
\pi
π
\newline
(D) The limit doesn't exist.
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Find
lim
x
→
∞
4
x
2
−
3
x
x
3
\lim _{x \rightarrow \infty} \frac{4 x^{2}-3 x}{x^{3}}
lim
x
→
∞
x
3
4
x
2
−
3
x
.
\newline
Choose
1
1
1
answer:
\newline
(A)
4
4
4
\newline
(B)
0
0
0
\newline
(C)
−
3
-3
−
3
\newline
(D) The limit is unbounded
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Find
lim
x
→
∞
−
4
x
3
+
5
x
2
x
3
+
7
\lim _{x \rightarrow \infty} \frac{-4 x^{3}+5 x}{2 x^{3}+7}
lim
x
→
∞
2
x
3
+
7
−
4
x
3
+
5
x
.
\newline
Choose
1
1
1
answer:
\newline
(A)
5
7
\frac{5}{7}
7
5
\newline
(B)
−
2
-2
−
2
\newline
(C)
0
0
0
\newline
(D) The limit is unbounded
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Find
lim
x
→
∞
3
x
3
−
5
x
x
3
−
2
x
2
+
1
\lim _{x \rightarrow \infty} \frac{3 x^{3}-5 x}{x^{3}-2 x^{2}+1}
lim
x
→
∞
x
3
−
2
x
2
+
1
3
x
3
−
5
x
\newline
Choose
1
1
1
answer:
\newline
(A)
−
5
-5
−
5
\newline
(B)
0
0
0
\newline
(C)
3
3
3
\newline
(D) The limit is unbounded
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Find the derivative of
f
(
x
)
f(x)
f
(
x
)
.
\newline
f
(
x
)
=
ln
(
x
)
f(x) = \ln(x)
f
(
x
)
=
ln
(
x
)
\newline
f
′
(
x
)
=
f'(x) =
f
′
(
x
)
=
______
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