Show that the function f(x) = x2 + sqrt7-x is continuous at x=4. | Mathematics I 2080

Mathematics I20805 marksNumerical: continuity of functionContinuity

Show that the function $f(x) = x^2 + \sqrt{7-x}$ is continuous at $x=4$ . [5]

Show that the function $f(x) = x^2 + \sqrt{7-x}$ is continuous at $x=4$. [5]

Function: $f(x) = x^2 + \sqrt{7 - x}$ - Point: $x = 4$ $f(x)$ is continuous at $x = a$ if all three hold: 1. $f(a)$ is defined 2. $\lim{x \to a} f(x)$ exists 3. $\lim{x \to a} f(x) = f(a)$ Here $a = 4$ . --- $f(4) = 4^2 + \sqrt{7 - 4} = 16 + \sqrt{3}$ Since $7 - 4 = 3 0$ , the square root is re...

Function: $f(x) = x^2 + \sqrt{7 - x}$ - Point: $x = 4$ $f(x)$ is continuous at $x = a$ if all three hold: 1. $f(a)$ is defined 2. $\lim{x \to a} f(x)$ exists 3. $\lim{x \to a} f(x) = f(a)$ Here $a = 4$. --- $$f(4) = 4^2 + \sqrt{7 - 4} = 16 + \sqrt{3}$$ Since $7 - 4 = 3 0$, the square root is re...