EXPLORING CONCEPTS Finding Functions Find differentiable functions f and g such that lim x → ∞ f ( x ) = lim x → ∞ g ( x ) ∞ and lim x → ∞ [ f ( x ) − g ( x ) ] = 25. Explain how you obtained your answers. (Note: There are many correct answers.)
Solution Summary: The author calculates the differential functions f and g that satisfy the provided condition.
Finding Functions Find differentiable functions f and g such that
lim
x
→
∞
f
(
x
)
=
lim
x
→
∞
g
(
x
)
∞
and
lim
x
→
∞
[
f
(
x
)
−
g
(
x
)
]
=
25.
Explain how you obtained your answers. (Note: There are many correct answers.)
With integration, one of the major concepts of calculus. Differentiation is the derivative or rate of change of a function with respect to the independent variable.
lim f(x) as x approaches infinity
lim f(x) as x approaches negative infinity
Sketching functionsa. Sketch the graph of a function that is not continuous at 1, but isdefined at 1.b. Sketch the graph of a function that is not continuous at 1, buthas a limit at 1.
A) If for a function f(x) the first and second derivatives at a point a are zero, is it possible that f(x) has a relative maximum at a? Reason your answer with an example.
B) Study the continuity and asymptotic behavior of the function:
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.