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

Step-by-step Solution

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Final Answer

$1$
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Step-by-step Solution

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Applying the tangent identity: $\displaystyle\tan\left(\theta\right)=\frac{\sin\left(\theta\right)}{\cos\left(\theta\right)}$

$\frac{\frac{\sin\left(x\right)}{\cos\left(x\right)}}{\sin\left(x\right)}$
Why is tan(x) = sin(x)/cos(x) ?

Learn how to solve limits by direct substitution problems step by step online.

$\frac{\frac{\sin\left(x\right)}{\cos\left(x\right)}}{\sin\left(x\right)}$

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Learn how to solve limits by direct substitution problems step by step online. Find the limit (x)->(0)lim(tan(x)/sin(x)). Applying the tangent identity: \displaystyle\tan\left(\theta\right)=\frac{\sin\left(\theta\right)}{\cos\left(\theta\right)}. Divide fractions \frac{\frac{\sin\left(x\right)}{\cos\left(x\right)}}{\sin\left(x\right)} with Keep, Change, Flip: \frac{a}{b}\div c=\frac{a}{b}\div\frac{c}{1}=\frac{a}{b}\times\frac{1}{c}=\frac{a}{b\cdot c}. Simplify the fraction \frac{\sin\left(x\right)}{\cos\left(x\right)\sin\left(x\right)} by \sin\left(x\right). Applying the trigonometric identity: \displaystyle\sec\left(\theta\right)=\frac{1}{\cos\left(\theta\right)}.

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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Function Plot

Plotting: $\frac{\tan\left(x\right)}{\sin\left(x\right)}$

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0
a
b
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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

How to improve your answer:

Main Topic: Limits by Direct Substitution

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

Used Formulas

1. See formulas

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