Question

Determine all numbers at which the function is continuous.

Answer 1

Answer:

B

Explanation:

`\lim_(x \to 5) (x^2-7x+10)/(x^2-14x+45)\\= \lim_(x \to 5) (x^2-2x-5x+10)/(x^2-5x-9x+45)  \\= \lim_(x \to 5)  (x(x-2)-5(x-2))/(x(x-5)-9(x-5)) \\= \lim_(x \to 5)((x-2)(x-5))/((x-5)(x-9)) \\= \lim_(x \to 5) (x-2)/(x-9)  \\=(5-2)/(5-9) \\=-(3)/(4)\\also~f(5)=-3/4\\so~ it~ is~ continuous~ at ~x=5`

it does not exist at x=9.

so it is not continuous at x=9