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Limits: Basics
Related Topics
Wize University Calculus 1 Textbook > Limits
Basics
2 Activities
Determine
lim
x
→
π
2
ln
(
sin
x
)
\displaystyle \lim_{x\to\frac{\pi}{2}}\ln\left(\sin x\right)
x
→
2
π
lim
ln
(
sin
x
)
.
a.
−
∞
-\infty
−
∞
(Does not exist)
b.
0
0
0
c.
1
+
1^+
1
+
d.
1
1
1
e.
π
2
\frac{\pi}{2}
2
π
I don't know
Check Submission
More Basics Questions:
Infinite Limits
Evaluate
lim
x
→
∞
arctan
(
x
−
x
3
)
\displaystyle \lim_{x\to\infty}\arctan\left(x-x^3\right)
x
→
∞
lim
arctan
(
x
−
x
3
)
Limits: Basics
lim
x
→
0
∣
2
x
−
1
∣
−
∣
2
x
+
1
∣
x
\displaystyle\lim_{x\rightarrow0}\dfrac{\lvert 2x-1\rvert-\lvert 2x+1\rvert}{x}
x
→
0
lim
x
∣
2
x
−
1
∣
−
∣
2
x
+
1
∣
Infinite Limits
Evaluate
lim
x
→
∞
arctan
(
x
−
x
3
)
\displaystyle \lim_{x\to\infty}\arctan\left(x-x^3\right)
x
→
∞
lim
arctan
(
x
−
x
3
)
Limit with Absolute Value
lim
x
→
0
∣
3
−
2
x
∣
−
∣
2
x
−
3
∣
x
=
\displaystyle\lim_{x\to0}\ \frac{\left|3-2x\right|-\left|2x-3\right|}{x}=
x
→
0
lim
x
∣
3
−
2
x
∣
−
∣
2
x
−
3
∣
=
Limits: Basics
lim
x
→
0
∣
2
x
−
1
∣
−
∣
2
x
+
1
∣
x
\displaystyle\lim_{x\rightarrow0}\dfrac{\lvert 2x-1\rvert-\lvert 2x+1\rvert}{x}
x
→
0
lim
x
∣
2
x
−
1
∣
−
∣
2
x
+
1
∣
Inverse Trig & Exponential Limits
Find the value of
lim
x
→
0
+
arctan
(
e
1
x
)
\displaystyle\lim_{x\rightarrow0^+}\arctan\left(e^{\frac{1}{x}}\right)
x
→
0
+
lim
arctan
(
e
x
1
)
.
Basic limit techniques - Absolute value
Evaluate
lim
x
→
4
−
∣
x
−
4
∣
x
2
−
4
.
\lim\limits_{x\rightarrow4^-}\frac{\vert x-4\vert}{x^2-4}.
x
→
4
−
lim
x
2
−
4
∣
x
−
4∣
.
Basic limit techniques - Absolute value
Evaluate
lim
x
→
4
−
∣
x
−
4
∣
x
2
−
4
.
\lim\limits_{x\rightarrow4^-}\frac{\vert x-4\vert}{x^2-4}.
x
→
4
−
lim
x
2
−
4
∣
x
−
4∣
.
Inverse Trig & Exponential Limits
Find the value of
lim
x
→
0
+
arctan
(
e
1
x
)
\displaystyle\lim_{x\rightarrow0^+}\arctan\left(e^{\frac{1}{x}}\right)
x
→
0
+
lim
arctan
(
e
x
1
)
.
Inverse Trig & Exponential Limits
Find the value of
lim
x
→
0
+
arctan
(
e
1
x
)
\displaystyle\lim_{x\rightarrow0^+}\arctan\left(e^{\frac{1}{x}}\right)
x
→
0
+
lim
arctan
(
e
x
1
)
.
Limits: Absolute Values
Q.
\textbf{Q.}
Q.
Evaluate
lim
x
→
0
∣
2
x
−
1
∣
−
∣
2
x
+
1
∣
x
\displaystyle \lim_{x\rightarrow 0}\frac{\lvert 2x-1\rvert-\lvert 2x+1\rvert}{x}
x
→
0
lim
x
∣
2
x
−
1
∣
−
∣
2
x
+
1
∣
.
Limit with Absolute Value
lim
x
→
0
∣
3
−
2
x
∣
−
∣
2
x
−
3
∣
x
=
\displaystyle\lim_{x\to0}\ \frac{\left|3-2x\right|-\left|2x-3\right|}{x}=
x
→
0
lim
x
∣
3
−
2
x
∣
−
∣
2
x
−
3
∣
=
Infinite Limits
Evaluate
lim
x
→
∞
arctan
(
x
−
x
3
)
\displaystyle \lim_{x\to\infty}\arctan\left(x-x^3\right)
x
→
∞
lim
arctan
(
x
−
x
3
)
Inverse Trig & Exponential Limits
Find the value of
lim
x
→
0
+
arctan
(
e
1
x
)
\displaystyle\lim_{x\rightarrow0^+}\arctan\left(e^{\frac{1}{x}}\right)
x
→
0
+
lim
arctan
(
e
x
1
)
.
Trigonometric Functions
Evaluate
lim
x
→
0
sin
(
1
∣
x
∣
)
\lim_{x\rightarrow0}\sin\left(\frac{1}{\left|x\right|}\right)
lim
x
→
0
sin
(
∣
x
∣
1
)
.
Limits: Absolute Values
Q.
\textbf{Q.}
Q.
Evaluate
lim
x
→
0
∣
2
x
−
1
∣
−
∣
2
x
+
1
∣
x
\displaystyle \lim_{x\rightarrow 0}\frac{\lvert 2x-1\rvert-\lvert 2x+1\rvert}{x}
x
→
0
lim
x
∣
2
x
−
1
∣
−
∣
2
x
+
1
∣
.
Basic limit techniques - Absolute value
Evaluate
lim
x
→
4
−
∣
x
−
4
∣
x
2
−
4
.
\lim\limits_{x\rightarrow4^-}\frac{\vert x-4\vert}{x^2-4}.
x
→
4
−
lim
x
2
−
4
∣
x
−
4∣
.
Limits: Basics
lim
x
→
0
∣
2
x
−
1
∣
−
∣
2
x
+
1
∣
x
\displaystyle\lim_{x\rightarrow0}\dfrac{\lvert 2x-1\rvert-\lvert 2x+1\rvert}{x}
x
→
0
lim
x
∣
2
x
−
1
∣
−
∣
2
x
+
1
∣
Limits: Basics
Determine
lim
x
→
π
2
ln
(
sin
x
)
\displaystyle \lim_{x\to\frac{\pi}{2}}\ln\left(\sin x\right)
x
→
2
π
lim
ln
(
sin
x
)
.
lim
x
→
0
∣
2
x
−
1
∣
−
∣
2
x
+
1
∣
x
\displaystyle\lim_{x\rightarrow0}\dfrac{\lvert 2x-1\rvert-\lvert 2x+1\rvert}{x}
x
→
0
lim
x
∣
2
x
−
1
∣
−
∣
2
x
+
1
∣