Looks like the given limit is
With some simple algebra, we can rewrite
then distribute the limit over the product,
The first limit is 0, since 1/3ⁿ is a positive, decreasing sequence. But before claiming the overall limit is also 0, we need to show that the second limit is also finite.
For the second limit, recall the definition of the constant, <em>e</em> :
To make our limit resemble this one more closely, make a substitution; replace 9/(<em>n</em> - 9) with 1/<em>m</em>, so that
From the relation 9<em>m</em> = <em>n</em> - 9, we see that <em>m</em> also approaches infinity as <em>n</em> approaches infinity. So, the second limit is rewritten as
Now we apply some more properties of multiplication and limits:
So, the overall limit is indeed 0:
1. Crippled, Disabled
Crippled is almost sound like a discriminating word and have a negative connotation where as disabled is more polished and reverent.
2. Relaxed, Easy-going
Both seem same but relaxed refers to free, pleasure and stress free but easy-going implies not serious and laziness.
3. Knockout, Beautiful
Knockout mainly used to imply someone is sex y where as beautiful is simple compliment for a person.
4. Young, Immature
Sometimes both are used in the same context but youth may be always a substitute for immature.
5. Skinny, Thi n Both are almost similar but actually someone skinny is called thin.
Answer:
√(V / π × h), where V is the volume of the cylinder, h is the height, and π(Pi) is a mathematical constant with an approximate value of 3.14