3 years ago

Which of the following relations is a function

Mathematics

2 answers:

ankoles [38]3 years ago

4 0

Answer: (-1,1)

Step-by-step explanation:

Natalija [7]3 years ago

3 0

Answer:

1st one

Step-by-step explanation:

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the sequence {a_n} is defined by a_1= 1 and a_(n+1) = 1/2( a_n+ (4/a_n) ) for >=1. Assuming that {a_n} converges, find its li

katen-ka-za [31]

$a_{n+1}=\dfrac{a_n+\frac4{a_n}}2$

Assuming convergence of the sequence, we have $a_n\to L$ for some limit $L$ as $n\to\infty$ . This also means $a_{n+1}\to L$ . So in the above equation, we can substitute and solve for $L$ :

$L=\dfrac{L+\frac4L}2$

$\implies2L^2=L^2+4$

$\implies L^2=4\implies L=\pm2$

The limit can only be one of these values; otherwise, the sequence would be divergent. To decide which one is correct, we can observe that the sequence is strictly positive. So $L=2$ .