When an electric current passes through two resistors with resistance r₁ and r₂, connected in parallel, the combined resistance, R, is determined by the equation 1/R = 1/r₁ + 1/r₂ , (R > 0, r₁ > 0, r₂ > 0). Assume that r₂ is constant, but r₁ changes.

Find the expression for R through r₁ and r₂ and demonstrate that R is an increasing function of r₁. You do not need to use derivative, give your analysis in words. Hint: a simple manipulation with the formula R = ... which you derive, will convert R to a form, from where the answer is clear. Make a sketch of R versus r₁ (show r₂ in the sketch). What is the practical value of R when the value of r₁ is very large?