What is the volume of the triangular Prism
1 answer:
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Answer with explanation:
Given the function f from R to
f:
To prove that the function is objective from R to
Proof:
When we prove the function is bijective then we proves that function is one-one and onto.
First we prove that function is one-one
Let
Cancel power on both side then we get
Hence, the function is one-one on domain [tex[(0,\infty)[/tex].
Now , we prove that function is onto function.
Let - f(x)=y
Then we get
The value of y is taken from
Therefore, we can find pre image for every value of y.
Hence, the function is onto function on domain
Therefore, the given is bijective function on
not on whole domain R .
Hence, proved.
Answer:
The answer is 48 units³
Step-by-step explanation:
If we simply draw out the region on the x-y plane enclosed between these lines we realize that,if we evaluate the integral the limits all in all cannot be constants since one side of the triangular region is slanted whose equation is given by y=x. So the one of the limit of one of the integrals in the double integral we need to evaluate must be a variable. We choose x part of the integral to have a variable limit, we could well have chosen y's limits as non constant, but it wouldn't make any difference. So the double integral we need to evaluate is given by,
Please note that the order of integration is very important here.We cannot evaluate an integral with variable limit last, we have to evaluate it first.after performing the elementary x integral we get,
After performing the elementary y integral we obtain the desired volume as below,