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Let’s check out your problem:
lim
x
→
0
cos
(
x
)
=
?
\lim _{x \rightarrow 0} \cos (x)=?
x
→
0
lim
cos
(
x
)
=
?
\newline
Choose
1
1
1
answer:
\newline
(A)
−
1
-1
−
1
\newline
(B)
0
0
0
\newline
(C)
1
1
1
\newline
(D) The limit doesn't exist.
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Math Problems
Calculus
Find derivatives of logarithmic functions
Full solution
Q.
lim
x
→
0
cos
(
x
)
=
?
\lim _{x \rightarrow 0} \cos (x)=?
x
→
0
lim
cos
(
x
)
=
?
\newline
Choose
1
1
1
answer:
\newline
(A)
−
1
-1
−
1
\newline
(B)
0
0
0
\newline
(C)
1
1
1
\newline
(D) The limit doesn't exist.
Evaluate the limit:
To solve the limit problem, we need to evaluate the limit of the cosine function as
x
x
x
approaches
0
0
0
.
lim
x
→
0
cos
(
x
)
=
cos
(
0
)
\lim_{x \to 0} \cos(x) = \cos(0)
x
→
0
lim
cos
(
x
)
=
cos
(
0
)
Cosine of
0
0
0
degrees:
We know from trigonometry that the cosine of
0
0
0
degrees (or
0
0
0
radians) is equal to
1
1
1
.
cos
(
0
)
=
1
\cos(0) = 1
cos
(
0
)
=
1
Limit of
cos
(
x
)
\cos(x)
cos
(
x
)
as
x
x
x
approaches
0
0
0
:
Therefore, the limit of
cos
(
x
)
\cos(x)
cos
(
x
)
as
x
x
x
approaches
0
0
0
is equal to
1
1
1
.
lim
x
→
0
cos
(
x
)
=
1
\lim_{x \to 0} \cos(x) = 1
lim
x
→
0
cos
(
x
)
=
1
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