D003함수의 합, 차, 곱, 몫의 극한값3년 연속

두 함수 $\displaystyle{f \left ( x \right ) }$, $\displaystyle{g \left ( x \right ) }$가

$\displaystyle{\lim \limits _{{x \rightarrow 1}} f \left ( x \right ) g \left ( x \right ) =4}$, $\displaystyle{\lim \limits _{{x \rightarrow 1}} \dfrac {{f \left ( x \right ) +g \left ( x \right ) }} {{f \left ( x \right ) }} =3}$

을 만족시킬 때, $\displaystyle{\lim \limits _{{x \rightarrow 1}} \left \{ \left ( f \left ( x \right ) \right ) ^{{2}} + \left ( g \left ( x \right ) \right ) ^{{2}} \right \} }$의 값을 구하시오.

두 함수 $\displaystyle f \left ( x \right )$, $\displaystyle g \left ( x \right )$에 대하여

$\displaystyle \lim \limits _{{x \rightarrow 2}} \left \{ f \left ( x \right ) -f \left ( x \right ) g \left ( x \right ) \right \} =3$, $\displaystyle \lim \limits _{{x \rightarrow 2}} \left \{ f \left ( x \right ) +f \left ( x \right ) g \left ( x \right ) \right \} =7$

일 때, $\displaystyle 5 \times \lim \limits _{{x \rightarrow 2}} \left \{ f \left ( x \right ) +g \left ( x \right ) \right \}$의 값을 구하시오.

두 함수 $\displaystyle{f(x), g(x)}$ 가

$\displaystyle{\lim _{x \rightarrow 1}\{f(x)-g(x)\}=-\frac{7}{6}, \lim _{x \rightarrow 1} f(x) g(x)=-\frac{1}{3}}$ 을 만족시킬 때, $\displaystyle{\lim _{x \rightarrow 1}\left\{\frac{1}{f(x)+g(x)}\right\}^{2}}$ 의 값을 구하시오.

두 함수 $\displaystyle f \left ( x \right )$, $\displaystyle g \left ( x \right )$가

$\displaystyle \lim \limits _{{x \rightarrow 2}} \left ( f \left ( x \right ) +g \left ( x \right ) \right ) =6$, $\displaystyle \lim \limits _{{x \rightarrow 2}} \left \{ \left ( f \left ( x \right ) \right ) ^{{2}} +f \left ( x \right ) g \left ( x \right ) \right \} =12$

를 만족시킬 때, $\displaystyle \lim \limits _{{x \rightarrow 2}} \left ( f \left ( x \right ) -g \left ( x \right ) \right )$의 값은?