Determine all real numbers a > 0 for which there exists a nonnegative alive continuous function f ( x ) defined on ⌈ 0 , a ⌉ with the property that the region R = { ( x , y ) ; 0 ≤ x ≤ a , 0 ≤ y ≤ f ( x ) } has perimeter k units and area k square units for some real number k
Determine all real numbers a > 0 for which there exists a nonnegative alive continuous function f ( x ) defined on ⌈ 0 , a ⌉ with the property that the region R = { ( x , y ) ; 0 ≤ x ≤ a , 0 ≤ y ≤ f ( x ) } has perimeter k units and area k square units for some real number k
Determine all real numbers
a
>
0
for which there exists a nonnegative alive continuous function f(x) defined on
⌈
0
,
a
⌉
with the property that the region
R
=
{
(
x
,
y
)
;
0
≤
x
≤
a
,
0
≤
y
≤
f
(
x
)
}
has perimeter k units and area k square units for some real number k
Use the properties of logarithms, given that In(2) = 0.6931 and In(3) = 1.0986, to approximate the logarithm. Use a calculator to confirm your approximations. (Round your answers to four decimal places.)
(a) In(0.75)
(b) In(24)
(c) In(18)
1
(d) In
≈
2
72
Find the indefinite integral. (Remember the constant of integration.)
√tan(8x)
tan(8x) sec²(8x) dx
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