<span>The y-intercept of is .
Of course, it is 3 less than , the y-intercept of .
Subtracting 3 does not change either the regions where the graph is increasing and decreasing, or the end behavior. It just translates the graph 3 units down.
It does not matter is the function is odd or even.
is the mirror image of stretched along the y-direction.
The y-intercept, the value of for , is</span><span>which is times the y-intercept of .</span><span>Because of the negative factor/mirror-like graph, the intervals where increases are the intervals where decreases, and vice versa.
The end behavior is similarly reversed.
If then .
If then .
If then .
The same goes for the other end, as tends to .
All of the above applies equally to any function, polynomial or not, odd, even, or neither odd not even.
Of course, if polynomial functions are understood to have a non-zero degree, never happens for a polynomial function.</span><span> </span>
The answer is (1/2)xe^(2x) - (1/4)e^(2x) + C
Solution:
Since our given integrand is the product of the functions x and e^(2x), we can use the formula for integration by parts by choosing
u = x
dv/dx = e^(2x)
By differentiating u, we get
du/dx= 1
By integrating dv/dx= e^(2x), we have
v =∫e^(2x) dx = (1/2)e^(2x)
Then we substitute these values to the integration by parts formula:
∫ u(dv/dx) dx = uv −∫ v(du/dx) dx
∫ x e^(2x) dx = (x) (1/2)e^(2x) - ∫ ((1/2) e^(2x)) (1) dx
= (1/2)xe^(2x) - (1/2)∫[e^(2x)] dx
= (1/2)xe^(2x) - (1/2) (1/2)e^(2x) + C
where c is the constant of integration.
Therefore,
∫ x e^(2x) dx = (1/2)xe^(2x) - (1/4)e^(2x) + C
Answer:
(-2,-2) and (3,4)
Step-by-step explanation:
Edge 2020
Answer: x=2/3
Step-by-step explanation:
Let r represent the radius of cylinder.
We have been given that the height of a right circular cylinder is 1.5 times the radius of the base. So the height of the cylinder would be 
.
We will use lateral surface area of pyramid to solve our given problem.
, where,
LSA = Lateral surface area of pyramid,
r = Radius,
h = height.
Upon substituting our given values in above formula, we will get:
Now we will find the total surface area of cylinder.
Therefore, the ratio of total surface area to lateral surface area is 
.
