Function and numerical sequence

1Find the domain of the function:

  1. y=\frac{x}{\sqrt{5-x}}
  2. y=(x-4)\cdot \sqrt{x+1}
  3. y=\frac{3}{x-1}
  4. y=\frac{3}{x^{2}+1}

2)Given functiony=1-x^{2}

  1. Study the monotony in R^{+} , R^{-}
  2. Make the graph and find the range.

3)Given the string with the formula : y_{n}=\sqrt{3+2n}

  1. Write : y3 ,yn-1, y3n , yn+4.
  2. Is 7 a number of the string?

4)In the geometric progression find  y1 and q when you know that  \left\{\begin{matrix} y_{3}-y_{1}=6\\ y_{3}=8 \end{matrix}\right.

5)In the geometric progression find  y1 and  dwhen you know that  y3=11 and S4=55

6)Is yn=5-2n geometric progression or arithmetic progression .Find S10.

7)Is  yn=(4)n  geometric progression or arithmetic progression. Find  S15.