no calculator is allowed on this question. f(x)=(2x² - 5x - 3)/(x² - 9) function f above, lim f(x)=k. what…
no calculator is allowed on this question. f(x)=(2x² - 5x - 3)/(x² - 9) function f above, lim f(x)=k. what is the value of k? x→3 2 1/3 7/6 0
Answer
Explanation:
Step1: Factor the numerator and denominator
First, factor (2x^{2}-5x - 3=(2x + 1)(x - 3)) and (x^{2}-9=(x + 3)(x - 3)). So (f(x)=\frac{(2x + 1)(x - 3)}{(x + 3)(x - 3)}).
Step2: Simplify the function
Cancel out the common - factor ((x - 3)) (since (x\to3) but (x\neq3)), then (f(x)=\frac{2x + 1}{x + 3}) for (x\neq3).
Step3: Calculate the limit
Substitute (x = 3) into (\frac{2x+1}{x + 3}), we get (\lim_{x\to3}f(x)=\frac{2\times3+1}{3 + 3}=\frac{6 + 1}{6}=\frac{7}{6}).
Answer:
(\frac{7}{6})