Question

The function $\lim_{x \rightarrow 1}f(x) = 2$ is not defined at $\lim_{x \rightarrow 1}f(x)$. The value which should be assigned to f at x = 0 so that it is continuous at x = 0, is

• A. $\lim_{x \rightarrow 0}\frac{|x|}{x} =$
• B. $\lim_{x \rightarrow 1}(3x^{2} + 4x + 5) =$
• C. $\lim_{x \rightarrow a}\frac{x^{n} - a^{n}}{x - a}$
• D. $na^{n - 1}$

Answer 1

Answer: (B)

$\lim_{x \rightarrow 1}(3x^{2} + 4x + 5) =$

Answer 2

Since limit of a function is $a + b$ as $x \rightarrow 0$, therefore to be continuous at $x = 0$, its value must be $a + b$ at

$x = 0 \Rightarrow f ( 0 ) = a + b$.