Fermi
·
Concept Library
·
Courses
·
Books
·
Problems
·
Simulations
·
Math Wiki
·
High School
Fermi
›
Problems
Mathematics
Mathematics
Problem
Consider the expression
f
(
x
)
=
sin
2
(
5
x
)
+
cos
2
(
3
x
)
−
1
f(x)=\sin^{2}(5x)+\cos^{2}(3x)-1
f
(
x
)
=
sin
2
(
5
x
)
+
cos
2
(
3
x
)
−
1
. (a) Show that
−
1
≤
f
(
x
)
≤
1
-1\le f(x)\le 1
−
1
≤
f
(
x
)
≤
1
for all real
x
x
x
. (b) Using the result from part (a), evaluate
lim
x
→
∞
sin
2
(
5
x
)
+
cos
2
(
3
x
)
−
1
x
2
\displaystyle \lim_{x \to \infty} \dfrac{\sin^{2}(5x)+\cos^{2}(3x)-1}{x^{2}}
x
→
∞
lim
x
2
sin
2
(
5
x
)
+
cos
2
(
3
x
)
−
1
.
Browse the problem library