Fermi
·
Concept Library
·
Courses
·
Books
·
Problems
·
Simulations
·
Math Wiki
·
High School
Fermi
›
Problems
Mathematics
Mathematics
Problem
Which of the following limits equals the instantaneous rate of change of a differentiable function
f
f
f
at
x
=
a
x=a
x
=
a
? a)
lim
h
→
0
f
(
a
+
h
)
−
f
(
a
)
a
+
h
\displaystyle \lim_{h\to 0}\frac{f(a+h)-f(a)}{a+h}
h
→
0
lim
a
+
h
f
(
a
+
h
)
−
f
(
a
)
b)
lim
h
→
0
f
(
a
+
h
)
−
f
(
a
−
h
)
h
\displaystyle \lim_{h\to 0}\frac{f(a+h)-f(a-h)}{h}
h
→
0
lim
h
f
(
a
+
h
)
−
f
(
a
−
h
)
c)
lim
h
→
0
f
(
a
+
h
)
−
f
(
a
)
h
\displaystyle \lim_{h\to 0}\frac{f(a+h)-f(a)}{h}
h
→
0
lim
h
f
(
a
+
h
)
−
f
(
a
)
d)
lim
x
→
a
f
(
a
)
−
f
(
x
)
x
−
a
\displaystyle \lim_{x\to a}\frac{f(a)-f(x)}{x-a}
x
→
a
lim
x
−
a
f
(
a
)
−
f
(
x
)
Browse the problem library