The derivative of the function g(x) as given in the task content by virtue of the Fundamental theorem of calculus is; g'(x) = √2 ln(t) dt = 1.
<h3>What is the derivative of the function g(x) by virtue of the Fundamental theorem of calculus as given in the task content?</h3>
g(x) = Integral; √2 ln(t) dt (with the upper and lower limits e^x and 1 respectively).
Since, it follows from the Fundamental theorem of calculus that given an integral where;
Now, g(x) = Integral f(t) dt with limits a and x, it follows that the differential of g(x);
g'(x) = f(x).
Consequently, the function g'(x) which is to be evaluated in this scenario can be determined as:
g'(x) = 
= 1
The derivative of the function g(x) as given in the task content by virtue of the Fundamental theorem of calculus is; g'(x) = √2 ln(t) dt = 1.
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Answer:
5 faces
Step-by-step explanation:
<u><em>Faces:</em></u>
=> 1 rectangular face+4 triangular face = 5 faces
Answer:
<h2>2</h2>
Step-by-step explanation:
Given g(x)=5x-4 and g(x)=f^{-1}(x)-3
Substituting g(x) = 5x-4 into the second equation we have;
5x-4 = f^{-1}(x)-3
f^{-1}(x) = 5x-4+3
f^{-1}(x) = 5x-1
To get f(x), let us first make y to be equal f^{-1}(x)
y = 5x-1
expressing x in terms of y to get f(x), we have;
5x = y+1
x = y/5+1/5
replacing y with x, we will have;
y = x/5 + 1/5
F(x) = x/5 + 1/5
Comparing x/5 + 1/5 with ax+b, a = 1/5 and b = 1/5
5a + 5b = 5(1/5)+ 5(1/5)
5a+5b = 1+1
5a+5b = 2
Answer:
50.24
Step-by-step explanation:
8÷2 is the radius. 3.14×4^2=50.24 m^2
^= where the exponent is supposed to go
Answer:
14
Step-by-step explanation:
k
=
c
−
b
2
4
a
We know that
a
=
1
,
b
=
−
8
and
c
=
2
, so let's substitute:
k
=
2
−
(
−
8
)
2
4
(
1
)
=
2
−
64
4
=
2
−
16
=
−
14
.
So, we have
min
=
−
14
. Let's check:
graph{(x^2 - 8x + 2 - y)(-14 -y)=0 [-11.82, 20.22, -15.38, 0.64]}
