Proof Prove that if the limit of f ( x ) as x approaches c exists, then the limit must be unique. [ Hint: Let lim x → 0 f ( x ) = L 1 , and lim x → 0 f ( x ) = L 2 , and prove that L 1 = L 2 .]
Proof Prove that if the limit of f ( x ) as x approaches c exists, then the limit must be unique. [ Hint: Let lim x → 0 f ( x ) = L 1 , and lim x → 0 f ( x ) = L 2 , and prove that L 1 = L 2 .]
Solution Summary: The author explains that the limit of a function f(x) as x approaches c must be unique.
Proof Prove that if the limit of f(x) as x approaches c exists, then the limit must be unique. [Hint: Let
lim
x
→
0
f
(
x
)
=
L
1
, and
lim
x
→
0
f
(
x
)
=
L
2
, and prove that
L
1
=
L
2
.]
Use the information to find and compare Δy and dy. (Round your answers to four decimal places.)
y = x4 + 7 x = −3 Δx = dx = 0.01
Δy =
dy =
4. A car travels in a straight line for one hour. Its velocity, v, in miles per hour at six minute intervals is shown
in the table. For each problem, approximate the distance the car traveled (in miles) using the given method,
on the provided interval, and with the given number of rectangles or trapezoids, n.
Time (min) 0 6 12 18|24|30|36|42|48|54|60
Speed (mph) 0 10 20 40 60 50 40 30 40 40 65
a.) Left Rectangles, [0, 30] n=5
b.) Right Rectangles, [24, 42] n=3
c.) Midpoint Rectangles, [24, 60] n=3
d.) Trapezoids, [0, 24] n=4
The bracket BCD is hinged at C and attached to a control cable at B. Let F₁ = 275 N and F2 = 275 N.
F1
B
a=0.18 m
C
A
0.4 m
-0.4 m-
0.24 m
Determine the reaction at C.
The reaction at C
N Z
F2
D
Chapter 1 Solutions
WebAssign Printed Access Card for Larson/Edwards' Calculus, 11th Edition, Single-Term
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