If `f(x)={2x^2+k\ \ \ \ ,\ \ \ \ if\ xgeq0-2x^2+k\ \ \ \ ,\ \ \ \ if\ x<0` , then what should be the value of `k` so that `f(x)` is continuous at `x=0` .

Determine the value(s) of constant(s) involved in the definition so that the given function is continuous: f(x)={k(x^2+3)\ \ \ ,\ \ \ if\ x<0 and\ \ \ \ \cos2x\ \ \ ,\ \ \ if\ xgeq0

Find the points of discontinuity, if any, of the following function: f(x)={(sinx)/x\ \ \ ,\ \ \ if\ x<0 2x+3\ \ \ ,\ \ \ xgeq0

Prove that the function f(x)={(sinx)/x\ \ \ ,\ \ \ x<0\ \ \ \ \x+1\ \ \ ,\ \ \ xgeq0 is everywhere continuous.

Determine the value of the constant m so that the function f(x)={m(x^2-2x)\ \ \ \ \ if\ x<0,\ \ \ cosx \ \ if\ xgeq0 is continuous.

Prove that the function f(x)={(sinx)/x\ \ \ ,\ \ \ x<0,\ \x+1\ \ \ ,\ \ \ xgeq0 is everywhere continuous.

Find the value of the constant k so that the given function is continuous at the indicated point: f(x)={k(x^2-2x),\ \ \ if\ x<0cosx ,\ \ \ if\ xgeq0 at x=0

Let f(x)={x^3+x^2+10 x ,\ \ x<0-3sinx ,\ \ \ \ xgeq0 . Investigate x=0 for local maxima/minima.

Discuss the continuity of f(x)={2x-1,\ \ \ x<0 ; {2x+1,\ \ \ xgeq0 at x=0

If (x)={2x^(2)+kquad ,quad if x>=0-2x^(2)+k,quad if x<0 then what should be the value of k so that f(x) is continuous at x=0.

If f(x) = {(x^2+k,,,x ge 0),(-x^2-k,,,x lt 0):} is continuous at x = 0, then k is equal to