Question

Hello Teacher, Could you help me with this equation?​

Answer 1

`(1)/(42)`

Explanation:

Since
`(√(0+9)-3 )/(sin7n) = (0)/(0)`

We should apply the L'Hopital Rule to find the limit. (Use this when we see
`(0)/(0)`.

Take the derivative of the numerator and the denominator individually.

`(d)/(dn) (√(n+9)-3) =`
`(1)/(2√(n+9) )`

`(d)/(dn)(sin7n)`
`= 7cos(7n)`

So the new equation is:

`(1)/(14cos(7n)√(n+9))`

Now we can plug in n = 0 into the new equation:

`(1)/(14cos(7*0)√(0+9))`

Since
`cos(7*0) = cos(0) = 1`

`(1)/(14*1√(9))`

`(1)/(14*3) = (1)/(42)`

Therefore the answer is
`(1)/(42)`.