Question

Evaluate $\underset{x\to 5}{lim}\frac{x^2-9x+20}{x-\left[x\right]}$

• A. 1
• B. 0
• C. -1
• D. does not exist

Answer 1

Answer: (D)

does not exist

$\underset{x\to 5}{lim}\frac{x^2-9x+20}{x-\left[x\right]}=\underset{x\to 5}{lim}\frac{(x-5)(x-4)}{x-\left[x\right]}x=5+h\Rightarrow \left[x\right]=5x=5-h\Rightarrow \left[x\right]=4\therefore R.H.L=1,L.H.L=0$
Hence limit does not exists