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![[IIT 1981] Is it true that limits of f(x) & g(x) when x tends to 0 exist under following condition?](https://i.ytimg.com/vi/vmX--vAr4eg/hq720.jpg?sqp=-oaymwE9COgCEMoBSFryq4qpAy8IARUAAAAAGAElAADIQj0AgKJDeAHwAQH4Af4JgALQBYoCDAgAEAEYZSBlKGUwDw==&rs=AOn4CLAsSUo2XP85QsREBw0YLPxVwDFDDA)
[IIT 1981] Is it true that limits of f(x) & g(x) when x tends to 0 exist under following condition?
![[IIT 1983] Find f](https://i.ytimg.com/vi/5XGGC7MQqao/hq720.jpg?sqp=-oaymwE9COgCEMoBSFryq4qpAy8IARUAAAAAGAElAADIQj0AgKJDeAHwAQH4Af4JgALQBYoCDAgAEAEYZSBlKGUwDw==&rs=AOn4CLD7E2L2a3E5QPPSzFAKI2PCEctffg)
[IIT 1983] Find f ' (0+) and f ' (0-) where f(x) is defined as follows.
![[IIT 1979] Find the value of f](https://i.ytimg.com/vi/EXgEGymYtDs/hq720.jpg?sqp=-oaymwEjCOgCEMoBSFryq4qpAxUIARUAAAAAGAElAADIQj0AgKJDeAE=&rs=AOn4CLDql9NBP6tltgzFfAlA_dQCqrzYBg)
[IIT 1979] Find the value of f ' (1) fiven the following definition of x.
![[IIT 1981] Find the limit of g[f(x)] as x tends to 0 where f(x) and g(x) are defined as follows.](https://i.ytimg.com/vi/AYnuvKFHdo8/hq720.jpg?sqp=-oaymwE9COgCEMoBSFryq4qpAy8IARUAAAAAGAElAADIQj0AgKJDeAHwAQH4Af4JgALQBYoCDAgAEAEYZSBlKGUwDw==&rs=AOn4CLDrXs_mnvbGyLPJLKwrVKtg3T8SOQ)
[IIT 1981] Find the limit of g[f(x)] as x tends to 0 where f(x) and g(x) are defined as follows.
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