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Find the limit $\lim_{x\to1}\left(\frac{\frac{x}{2x-2}\left(e^x-e\right)}{x}\right)$

Step-by-step Solution

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Final Answer

$\frac{e}{2}$
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Step-by-step Solution

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Multiplying the fraction by $e^x-e$

$\lim_{x\to1}\left(\frac{\frac{x\left(e^x-e\right)}{2x-2}}{x}\right)$

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

$\lim_{x\to1}\left(\frac{\frac{x\left(e^x-e\right)}{2x-2}}{x}\right)$

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Learn how to solve limits by direct substitution problems step by step online. Find the limit (x)->(1)lim((x/(2x-2)(e^x-e))/x). Multiplying the fraction by e^x-e. Divide fractions \frac{\frac{x\left(e^x-e\right)}{2x-2}}{x} 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{x\left(e^x-e\right)}{\left(2x-2\right)x} by x. If we directly evaluate the limit \lim_{x\to 1}\left(\frac{e^x-e}{2x-2}\right) as x tends to 1, we can see that it gives us an indeterminate form.

Final Answer

$\frac{e}{2}$

Exact Numeric Answer

$1.359141$

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Limits by Direct SubstitutionLimits by L'Hôpital's ruleLimits by FactoringLimits by Rationalizing

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Function Plot

Plotting: $\frac{e}{2}$

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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

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

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