Question

Urgent plss! Thanks For the answers​

Answer 1

Answer: B) 4/3

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Work Shown:

`\displaystyle \lim_(x \to 3) (f^2(x)-4)/(f^2(x)-f(x)-2)\\\\\\\displaystyle \lim_(x \to 3) ((f(x)-2)(f(x)+2))/((f(x)-2)(f(x)+1))\\\\\\\displaystyle \lim_(x \to 3) (f(x)+2)/(f(x)+1)\\\\\\\displaystyle (f(3)+2)/(f(3)+1)\\\\\\\displaystyle (2+2)/(2+1)\\\\\\\displaystyle (4)/(3)\\\\\\`

Notes:

In step 2, I used the difference of squares rule to factor the numerator. The denominator can be factored through trial and error. The key here is the f(x)-2 terms that show up in each. Those factors cancel in step 3.

Afterward, we apply the substitution rule,
`\displaystyle \lim_(x \to a) f(x) = f(a)`, so basically I plugged in x = 3. Then evaluated f(3) = 2 due to the point (3,2).