Step-by-step Solution

Evaluate the limit of $x^2+8x-9$ as $x$ approaches $5$

Go!
1
2
3
4
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
|◻|
=
>
<
>=
<=
sin
cos
tan
cot
sec
csc

asin
acos
atan
acot
asec
acsc

sinh
cosh
tanh
coth
sech
csch

asinh
acosh
atanh
acoth
asech
acsch

Final Answer

$\frac{7}{15}$$\,\,\left(\approx 0.4666666666666667\right)$

Step-by-step explanation

Problem to solve:

$\lim_{x\to5}\left(\frac{x^2+8x-9}{x^3-x^2+5x-5}\right)$

Choose the solving method

1

Evaluate the limit $\lim_{x\to5}\left(\frac{x^2+8x-9}{x^3-x^2+5x-5}\right)$ by replacing all occurrences of $x$ by $5$

$\frac{5^2+8\cdot 5-9}{5^3-1\cdot 5^2+5\cdot 5-5}$
2

Simplifying, we get

$\frac{7}{15}$

Final Answer

$\frac{7}{15}$$\,\,\left(\approx 0.4666666666666667\right)$
$\lim_{x\to5}\left(\frac{x^2+8x-9}{x^3-x^2+5x-5}\right)$

Time to solve it:

~ 0.05 s (SnapXam)