Writing a Limit as a Definite Integral In Exercises 11-14, write the limit as a definite integral on the given interval, where c i is any point in the ith subinterval. lim ‖ Δ ‖ → 0 ∑ i = 1 n ( 1 + 3 c i ) Δ x i , [ 1 , 5 ]
Writing a Limit as a Definite Integral In Exercises 11-14, write the limit as a definite integral on the given interval, where c i is any point in the ith subinterval. lim ‖ Δ ‖ → 0 ∑ i = 1 n ( 1 + 3 c i ) Δ x i , [ 1 , 5 ]
Solution Summary: The author explains the formula used to calculate the definite integral of f(x).
Writing a Limit as a Definite Integral In Exercises 11-14, write the limit as a definite integral on the given interval, where
c
i
is any point in the ith subinterval.
lim
‖
Δ
‖
→
0
∑
i
=
1
n
(
1
+
3
c
i
)
Δ
x
i
,
[
1
,
5
]
With differentiation, one of the major concepts of calculus. Integration involves the calculation of an integral, which is useful to find many quantities such as areas, volumes, and displacement.
mate
hat is the largest area that can be en
18 For the function y=x³-3x² - 1, use derivatives to:
(a) determine the intervals of increase and decrease.
(b) determine the local (relative) maxima and minima.
(c) determine the intervals of concavity.
(d) determine the points of inflection.
b)
(e) sketch the graph with the above information indicated on the graph.
use L'Hopital Rule to evaluate the following.
a) 4x3 +10x2
23009׳-9
943-9
b) hm
3-84
хто бу+2
< xan
x-30650)
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