evaluate the following limits lim x tends to 0 root5-root4+cosx/3sin^2
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Answer:
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Calculus Examples
Popular Problems Calculus Evaluate ( limit as x approaches 0 from the right of sin(x))/(5 square root of x)
lim
x
→
0
+
sin
(
x
)
5
√
x
Change the two-sided limit into a right sided limit.
lim
x
→
0
+
sin
(
x
)
5
√
x
Move the term
1
5
outside of the limit because it is constant with respect to
x
.
1
5
lim
x
→
0
+
sin
(
x
)
√
x
Evaluate the limit of the numerator and the limit of the denominator.
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1
5
⋅
0
0
Since
0
0
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
→
0
+
sin
(
x
)
√
x
=
lim
x
→
0
+
d
d
x
[
sin
(
x
)
]
d
d
x
[
√
x
]
Find the derivative of the numerator and denominator.
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1
5
lim
x
→
0
+
cos
(
x
)
1
2
x
1
2
Since its numerator approaches a real number while its denominator is unbounded, the fraction
cos
(
x
)
1
2
x
1
2
approaches
0
.
1
5
⋅
0
Multiply
1
5
by
0
.
0
Answer:
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Step-by-step explanation:
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