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Function and numerical sequence

Function and numerical sequence

Categories MATH
Date 07/08/2022
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1Find the domain of the function:

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

2)Given function: $y=1-x^{2}$

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

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

Write : y₃ ,y_n-1, y₃_n , y_n+4.
Is 7 a number of the string?

4)In the geometric progression find y_{1 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 y_{1 and} dwhen you know that y₃=11 and S₄=55

6)Is y_n=5-2n geometric progression or arithmetic progression .Find S₁_0.

7)Is y_n=(4)ⁿ geometric progression or arithmetic progression. Find S_15.

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