Answer:
alalalalalalalalaa
Step-by-step explanation:
The missing parts of the table for the function are 49, 1 and 49 respectively
<h3>How to complete the missing parts of the table?</h3>
An exponential function is a type of function which involves exponents. A simple exponential function is of the form y = bˣ
Given: the exponential function y = (1/7)ˣ
In order to find the missing parts, we have to substitute the relevant values into the function. Thus:
For x = -2:
y = (1/7)ˣ
Substitute x = -2 into the function:
y = (1/7)⁻² = 49
For x = 0:
y = (1/7)ˣ
Substitute x = 0 into the function:
y = (1/7)⁰ = 1
For x = 2:
y = (1/7)ˣ
Substitute x = 2 into the function:
y = (1/7)² = 1/49
The missing part is 49
Therefore, the missing parts of the table are 49, 1 and 49 respectively
Learn more about exponential function on:
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Answer:
∫▒〖arctan(x).1 dx=arctan(x).x〗-1/2 ln(1+x^2 )+C
Step-by-step explanation:
∫▒〖1st .2nd dx=1st∫▒〖2nd dx〗-∫▒〖(derivative of 1st) dx∫▒〖2nd dx〗〗〗
Let 1st=arctan(x)
And 2nd=1
∫▒〖arctan(x).1 dx=arctan(x) ∫▒〖1 dx〗-∫▒〖(derivative of arctan(x))dx∫▒〖1 dx〗〗〗
As we know that
derivative of arctan(x)=1/(1+x^2 )
∫▒〖1 dx〗=x
So
∫▒〖arctan(x).1 dx=arctan(x).x〗-∫▒〖(1/(1+x^2 ))dx.x〗…………Eq1
Let’s solve ∫▒(1/(1+x^2 ))dx by substitution now
Let 1+x^2=u
du=2xdx
Multiply and divide ∫▒〖(1/(1+x^2 ))dx.x〗 by 2 we get
1/2 ∫▒〖(2/(1+x^2 ))dx.x〗=1/2 ∫▒(2xdx/u)
1/2 ∫▒(2xdx/u) =1/2 ∫▒(du/u)
1/2 ∫▒(2xdx/u) =1/2 ln(u)+C
1/2 ∫▒(2xdx/u) =1/2 ln(1+x^2 )+C
Putting values in Eq1 we get
∫▒〖arctan(x).1 dx=arctan(x).x〗-1/2 ln(1+x^2 )+C (required soultion)
Step-by-step explanation:
The answer is mentioned above.
