If f(x)=xsin 1x for x≠q 0 and f(0)=0 then, limlimits _(x→ 0)f(x)=0=f(0)Thus, this function is continuous at 0. In (A), limlimits _(x→ 0)sin 1x does not exist; in (B), f has aremovable discontinuity; and in (D), f has an infinite discontinuity.反馈 收藏 ...
(x) .T→c x→c+x→c T →C(c)I f the function is differentiable at r = c, then it has a horizontal tangent line at r = c.(d) I f lim f(r) and lim f(r) exist and lim f(r)≠ lim f(r), then f has a non-removable→c xc+x→c x→c+discontinuity at r = c...
A function f has the derivative shown. Which of the following statements must be false? ( ) A. f is continuous at x=a B. f has a vertical asymptote at x=a C. f has a jump discontinuity at x=a D. f has a removable discontinuity at x=a...
If f(x)=sgn(cos2x−2sinx+3), where sgn () is the signum function, then f(x) Ais continuous over its domain Bhas a missing point discontinuity Chas isolated point discontinuity Dhas irremovable discontinuitySubmit f(x)=sgn(cot−1x),g(x)=sgn(x2−4x+5) View Solution If f(...
Piecewise functions in which each branch is defined by a polynomial function can only be discontinuous at the values where the expression of the function changes, remember that polynomial functions are always continuous. Answer and Explanation...
Determine if the function f(x) = \begin{cases} (x^{2} - 25)/(x + 5), x \neq -5\-10, x = -5 \end{cases} is continuous at the point where x = -5. a) The function has a removable discontinuity at Determine if the given function is continuous. f (x...
Step by step video, text & image solution for Which of the following f has removable discontinuity at x=x_0? If the discontinuity is removable, find a function g that agrees with f for x ne x_0 and is continuous on R. f(x)=(3-sqrtx)/(9-x),x_0=9 by Maths experts to help...