lim x tends to 7 [x^3-343/√x-√7]
Answers
Step-by-step explanation:
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Calculus Examples
Popular Problems Calculus Evaluate ( limit as x approaches -7 of x^3+343)/(x+7)
lim
x
→
−
7
x
3
+
343
x
+
7
limx→-7x3+343x+7
Evaluate the limit of the numerator and the limit of the denominator.
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0
0
00
Since
0
0
00 is of indeterminate form, apply L'Hospital's Rule. L'Hospital's Rule states that the limit of a quotient of functions is equal to the limit of the quotient of their derivatives.
lim
x
→
−
7
x
3
+
343
x
+
7
=
lim
x
→
−
7
d
d
x
[
x
3
+
343
]
d
d
x
[
x
+
7
]
limx→-7x3+343x+7=limx→-7ddx[x3+343]ddx[x+7]
Find the derivative of the numerator and denominator.
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lim
x
→
−
7
3
x
2
1
limx→-73x21
Take the limit of each term.
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3
(
lim
x
→
−
7
x
)
2
lim
x
→
−
7
1
3(limx→-7x)2limx→-71
Evaluate the limits by plugging in
−
7
-7 for all occurrences of
x
x.
3
(
−
7
)
2
1
3(-7)21
Simplify the answer
147
147
Step-by-step explanation:
We have,
To find, the value of = ?
∴
=
Dividing numerator and denominator by (x - 7), we get