finite Geometric Sequences ercise 4: (answers on page 341 ) Determine the sum of each of the following infinite geometric sequences below: \( \begin{array}{ll}\text { a) } 5+\frac{5}{2}+\frac{5}{4}+\ldots & \text { c) } 20+2+0,2+\ldots \\ \text { b) } 6 x-2 x+\frac{2 x}{3}-\ldots & \text { d) } \sum_{x=1}^{\infty} 2^{1-x}\end{array} \)

3. (20б) Постройте область: \( \left\{\begin{array}{l}1<|z-3-i| \leq 2 \\ \arg z \geq-\frac{\pi}{6}\end{array}\right. \)

1. In electricity, the impe circuit is given by the \( \sqrt{R^{2}+\left(\omega L-\frac{1}{\omega C}\right)^{2}} \) a) Make \( C \) the subject of b) Find \( C \) when \( Z=120 \), \( 310 \quad \) and \( L=0.35 \).

4. (a) Sketch the curve with equation \[ y=a^{-x}+4 \]

If \( f(x)=\frac{\sqrt{x+2}}{3-3 x^{2}} \), for which values of \( x \) is 1.2.2 \( \quad f(x) \) non real.

a) Sketch the curve with equation \[ y=a^{-x}+4 \] where \( a \) is a constant and \( a>1 \) On your sketch show