Estimating limits graphically and numerically Use a graph of f estimate lim x → a f ( x ) or to show that the limit does not exist. Evaluate f ( x ) near x = a to support your conjecture. 29. f ( x ) = 1 − cos ( 2 x − 2 ) ( x − 1 ) 2 ; a = 1
Estimating limits graphically and numerically Use a graph of f estimate lim x → a f ( x ) or to show that the limit does not exist. Evaluate f ( x ) near x = a to support your conjecture. 29. f ( x ) = 1 − cos ( 2 x − 2 ) ( x − 1 ) 2 ; a = 1
Estimating limits graphically and numerically Use a graph of f estimate
lim
x
→
a
f
(
x
)
or to show that the limit does not exist. Evaluate f(x) near x = a to support your conjecture.
29.
f
(
x
)
=
1
−
cos
(
2
x
−
2
)
(
x
−
1
)
2
;
a
=
1
Use properties of limits and algebraic methods to find the limit, if it exists.
lim x→−3
x2 − 9
x + 3
Step 1
We want to use properties of limits and algebraic methods to find
lim x→−3
x2 − 9
x + 3
.
Note that the function is a function. The numerator and denominator are 0 at
x =
,
and thus we have the indeterminate form at
x =
.
We can factor
from the numerator and reduce the fraction.
lim x→−3
x2 − 9
x + 3
=
lim x→−3
(x − 3)
x + 3
=
lim x→−3
=
− 3
=
Given lim (4x-3) as x approaches 1.
Use the definition of a limt to find a number delta such that the absolute value of x-a is less than delta when the absolute value of f(x)-L is less than 0.08
lim_(h->0)(h)/(sin (3h))
Find the limit algebraically, h approaching zero from the left hand side
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.