Find k for which f(x) = \(\begin{cases}k + x, & x = 1\\4x + 3, & x \n

1.	Find k for which f(x) = \(\begin{cases}k + x, & x = 1\\4x + 3, & x \neq 1\end{cases}\) is continuous at x = 1.
Answer» \(\lim\limits_{x \to 1}f(x) = \lim\limits_{x \to 1}\)(4x + 3) = 4 + 3 = 7 since f(x) is continuous at x = 1 \(\lim\limits_{x \to 1}f(x) \) = f(1) 7 = k + 1; k = 7 - 1 = 6

Find k for which f(x) = \(\begin{cases}k + x, & x = 1\\4x + 3, & x \neq 1\end{cases}\) is continuous at x = 1.

Answer»

\(\lim\limits_{x \to 1}f(x) = \lim\limits_{x \to 1}\)(4x + 3)

= 4 + 3 = 7

since f(x) is continuous at x = 1

\(\lim\limits_{x \to 1}f(x) \) = f(1)

7 = k + 1;

k = 7 - 1 = 6

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