Math  /  Calculus

QuestionC/Jsers/ahmad/Downloads/4507091111202211\%20(1).pdf 9) If f(x)={x29x+3x3cx=3f(x)=\left\{\begin{array}{ll}\frac{x^{2}-9}{x+3} & x \neq-3 \\ c & x=-3\end{array}\right.
If f(x)f(x) is continuous for all xRx \in R, then c=c= a) 3 b) 6 c) 0 d) -6 10) If y=7y=7 is a horizontal asymptote of a rational function f(x)f(x), then which of the following must be true : a) limx7f(x)=\lim _{x \rightarrow 7} f(x)=\infty b) limxf(x)=7\lim _{x \rightarrow \infty} f(x)=7 c) limx0f(x)=7\lim _{x \rightarrow 0} f(x)=7 d) limx7f(x)=0\lim _{x \rightarrow 7} f(x)=0

Studdy Solution
لكي تكون الدالة متصلة عند x=3x=-3، يجب أن يكون:
limx3f(x)=f(3)=c\lim_{x \to -3} f(x) = f(-3) = c
وبما أننا وجدنا أن limx3f(x)=6\lim_{x \to -3} f(x) = -6، فإن:
c=6c = -6
الإجابة الصحيحة هي:
d)6\boxed{d) -6}

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