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. 30. f ( x ) = 3 sin x − 2 cos x + 2 x ; a = 0
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. 30. f ( x ) = 3 sin x − 2 cos x + 2 x ; a = 0
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.
Plot (using technology, like a graph calculator or Desmos) the function f(x) = tan(nx) for different values of n (positive, negative, x rational, irrational). Include some of the figures in your answer. Con- jecture what the limit of f(x) is as x approaches 0. Explain why you believe your conjecture is correct.
Question
For the function f(x): =
Provide your answer below:
a. lim f(x) =
x → 5
b. lim f(x) =
x → 5+
(2x² - 4x
-4x3
X
4.9
4.99
4.999
4.9999
4.99999
if x < 5
if x ≥ 5'
evaluate the left and right limits using the table shown below.
2x² - 4x
X
-4x - 3
28.42
5.1
-23.4
29.8402
5.01
-23.04
29.984002
5.001
-23.004
29.99840002
5.0001
-23.0004
29.9998400002
5.00001
-23.00004
Thomas' Calculus: Early Transcendentals (14th Edition)
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