CameraIcon
CameraIcon
SearchIcon
MyQuestionIcon


Question

If the function$$f(x)$$ satisfies $$\displaystyle \lim_{x\rightarrow 1}\frac{f\left ( x \right )-2}{x^{2}-1}=\pi $$ evaluate $$\displaystyle \lim_{x\rightarrow 1}f\left ( x \right )$$


Solution

$$\displaystyle \lim_{x\rightarrow 1}\frac{f\left ( x \right )-2}{x^{2}-1}=\pi $$
$$\displaystyle
\Rightarrow \frac{\lim_{x\rightarrow 1}\left ( f\left ( x \right )-2
\right )}{\lim_{x\rightarrow 1}\left ( x^{2} -1\right )}=\pi $$
$$\displaystyle
\Rightarrow \lim_{x\rightarrow 1}\left ( f\left ( x \right )-2 \right
)=\pi \lim_{x\rightarrow 1}\left ( x^{2}-1 \right )$$
$$\displaystyle \Rightarrow \lim_{x\rightarrow 1}\left ( f\left ( x \right )-2 \right )=\pi \left ( 1^{2}-1 \right )$$
$$\displaystyle \Rightarrow \lim_{x\rightarrow 1}\left ( f\left ( x \right )-2 \right )=0$$
$$\displaystyle \Rightarrow \lim_{x\rightarrow 1}f\left ( x \right )-\lim_{x\rightarrow 1}2=0$$
$$\displaystyle \Rightarrow \lim_{x\rightarrow 1}f\left ( x \right )-2=0$$
$$\displaystyle \therefore  \lim_{x\rightarrow 1}f\left ( x \right )=2$$

Mathematics
NCERT
Standard XI

Suggest Corrections
thumbs-up
 
0


similar_icon
Similar questions
View More


similar_icon
Same exercise questions
View More


similar_icon
People also searched for
View More



footer-image