To find the derivative, you must use the chain rule.
If u=x^3+2x:
dy/dx=(dy/du)(du/dx)
dy/du=d/du(e^u)=e^u=e^(x^3 + 2x)
du/dx =d/dx (x^3+2x) = 3x^2 + 2
So dy/dx=
e^(x^3+2x) * (3x^2+ 2)
The negative infinity for the x coordinate states that the graph should move to the bottom and the y coordinate is positive infinity so that the graph goes up
the first graph is your answer
You use the arithmetic sequence formula and input the information given to you.
tn = a + (n-1)d
t(56) is what your looking for so don't worry about the tn.
a is your first term,
a = 15.
n is the position of the term you are looking for, n = 56.
And d is the common difference, you find this by taking t2 and subtracting t1. t2=18 and t1=15.
d = 18 - 15 = 3
Inputting it all into the formula you get,
t(56) = 15 + (56-1)(3)
term 56 = 180.
You use this formula to find any term in a sequence provided you are given enough info. You can also manipulate it if you are asked to find something else like the first term(a), common difference(d) or term position(n). It just depends on what the question is asking and what information you are given. :)
Hope this helps!
First you do 3a^4(2b^6c^3)^2
=12a^4b^12c^6
<span>THE GIVEN QUESTION;
7x -3(4x-8) < 6x +12 - 9x
THE GIVEN INTERVAL OF X IS FROM [4,8] SO THE VALUE OF X ={4,5,6,7,8}
THE GIVEN QUESTION CAN BE EVALUATED TO
7x - 12x+ 24 < 12 - 3x
-5x + 24 < 12 - 3x //USING BODMAS RULE
NOW SUBSTITUTING THE VALUE OF X:
1) X=4 SOL: 4<0
2) X=5 SOL: -1<-3
3) X=6 SOL: -6<-6
4) X=7 SOL: -11<-9
5) X=8 SOL: -16<-12
HENCE THE VALUE OF X=7,8 SATISFY THE GIVEN INEQUALITY</span>