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.
Exercise 1
The given limit lim
h→0
2
(1+h) ³-1
h
Definition of the derivative
represents the derivative of a function y=f(x) at x = a. Find f (x) and a.
Solo
f (x, y) of a smooth real-valued function f defined on a bounded
Consider the graph z =
subset D of R². Show that the surface area of the graph is given by the formula:
1 +
dx dy.
ду
Surface area
Part (b)
Define a functiong : [0, 1) R by
tan(tx)
g (1) :=
-dx
x3/2
for all i € [0, 1).
(i)
Show that g is continuous on [0, 1).
(ii)
Show that g is differentiable on [0, 1).
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