Question

Lim √2x-1 -3 / x-5 tendendo x 5

Answer 1

Lim  [√(2x-1) -3] / (x-5)
x→5⁺

Lim  [√(2x-1) -3] *[√(2x-1) +3]/ (x-5)[√(2x-1) + 3]
x→5⁺

Lim  [√(2x-1)² -3²] / (x-5)[√(2x-1) + 3]
x→5⁺

Lim  [2x-10] / (x-5)[√(2x-1) + 3]
x→5⁺

Lim  2*[x-5] / (x-5)[√(2x-1) + 3]
x→5⁺

Lim    2/[√(2x-1) + 3]  =2/(√(10-1) +3)=2/(√(9) +3) =2/(3+3)=1/6=1/3
x→5⁺