Fermi
·
Concept Library
·
Courses
·
Books
·
Problems
·
Simulations
·
Math Wiki
·
High School
Fermi
›
Problems
Mathematics
Mathematics
Problem
Consider the function
g
(
x
)
=
sin
x
1
+
2
x
g(x)=\dfrac{\sin x}{1+2x}
g
(
x
)
=
1
+
2
x
sin
x
defined for all real
x
x
x
. a. (i) Find
g
′
(
x
)
g'(x)
g
′
(
x
)
. b. (ii) Evaluate
g
′
(
π
6
)
g'\!\left(\dfrac{\pi}{6}\right)
g
′
(
6
π
)
. c. (iii) Using the value obtained in part (ii), approximate the change in
g
(
x
)
g(x)
g
(
x
)
when
x
x
x
increases from
π
6
\dfrac{\pi}{6}
6
π
to
π
6
+
0.01
\dfrac{\pi}{6}+0.01
6
π
+
0.01
.
Browse the problem library