List of top Engineering Mathematics Questions on Continuity asked in GATE AE

Let the function \( f(x) \) be defined as:
\[ f(x) = \begin{cases} A + x, & \text{if } x < 2 \\ 1 + x^2, & \text{if } x \geq 2 \end{cases} \] If the function \( f(x) \) is continuous at \( x = 2 \), the value of \( A \) should be _______.

Let the function \( f(x) \) be defined as: \[ f(x) = \begin{cases} A + x, & {if } x<2
1 + x^2, & {if } x \geq 2 \end{cases} \] If the function \( f(x) \) is continuous at \( x = 2 \), the value of \( A \) is \_\_\_\_\_.

Let the function \( f(x) \) be defined as: \[ f(x) = \begin{cases} A + x, & {if } x<2
1 + x^2, & {if } x \geq 2 \end{cases} \] If the function \( f(x) \) is continuous at \( x = 2 \), the value of \( A \) is \_\_\_\_\_.

Consider \[ f(x) = \begin{cases} x^2, & x < 0, \\[6pt] x, & x \ge 0. \end{cases} \] Which statements are correct?

If a monotonic and continuous function \(y=f(x)\) has exactly one root in the interval \(x_1<x<x_2\), then: