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Find the limit $\lim_{x\to0}\left(\frac{\sin\left(x\right)}{x}\right)$

Step-by-step Solution

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ln
log
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sin
cos
tan
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asin
acos
atan
acot
asec
acsc

sinh
cosh
tanh
coth
sech
csch

asinh
acosh
atanh
acoth
asech
acsch

Final Answer

$1$
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Step-by-step Solution

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1

Applying the Sandwich Theorem, which states that: Let $I$ be an interval that contains the point $c$, and let $f(x)$, $g(x)$, and $h(x)$ be functions defined on $I$. If for every $x$ not equal to $c$ in the interval $I$ we have $g(x)\leq f(x)\leq h(x)$ and also suppose that: $\displaystyle\lim_{x\to c}{g(x)}=\lim_{x\to c}{h(x)}=L$, then: $\displaystyle\lim_{x\to c}{f(x)}=L$

$1$

Final Answer

$1$

Exact Numeric Answer

$1$

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Limits by Direct SubstitutionLimits by L'Hôpital's ruleLimits by factoringLimits by rationalizing

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1
2
3
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5
6
7
8
9
0
a
b
c
d
f
g
m
n
u
v
w
x
y
z
.
(◻)
+
-
×
◻/◻
/
÷
2

e
π
ln
log
log
lim
d/dx
Dx
|◻|
θ
=
>
<
>=
<=
sin
cos
tan
cot
sec
csc

asin
acos
atan
acot
asec
acsc

sinh
cosh
tanh
coth
sech
csch

asinh
acosh
atanh
acoth
asech
acsch

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Main Topic: Limits by Direct Substitution

Find limits of functions at a specific point by directly plugging the value into the function.

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