for-what-value-or-values-of-the-constant-kk-if-any-is-the-function-gxgx-defined-

Question

For what value or values of the constant $k$ , if any, is the function $g (x)$ defined as $g of x equals 2 cases Case 1: sine x comma if x is less than 0 Case 2: k x squared comma if x is greater than or equal to 0$ , continuous at $x equals 0$ and differentiable at $x equals 0$ ?

Accepted Answer

Continuous: for any value of $k$

Differentiable: for no value of $k$

Answer

Continuous: for any value of $k$

Differentiable: for any value of $k$

Answer

Continuous: for no value of $k$

Differentiable: for no value of $k$

Answer

Continuous: for no value of $k$

Differentiable: for any value of $k$

For what value or values of the constant kk, if any, is the function g(x)g(x) defined as g(x)={sinx, if x<0kx2, if x≥0g(x)=\begin{cases}\sin x,\text{ if }x<0\\ kx^2,\text{ if }x\ge0\end{cases}, continuous at x=0x = 0 and differentiable at x=0x = 0?

For what value or values of the constant $k$ , if any, is the function $g (x)$ defined as $g of x equals 2 cases Case 1: sine x comma if x is less than 0 Case 2: k x squared comma if x is greater than or equal to 0$ , continuous at $x equals 0$ and differentiable at $x equals 0$ ?