Let f x - Bmatrix a- x-clendBmatrix - a - b - c epsilon - R if f x is discontinuous at x - c- and have a jump at x - c then the value of jump is -A- undefined

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Standard XII

Mathematics

Jump of a Discontinuity

Let f x = Bma...

Question

Let f(x) = ${\begin{matrix} a & x > c b & x \geq c \end{matrix}} : a, b, c ϵ - R$
if f(x) is discontinuous at x = c, and have a jump at x = c then the value of jump is -
undefined

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Solution

It is given that the function is discontinuous at x = c, the jump will be nothing but the difference (modulus) of $∣ ∣ ∣ l i m x \to c^{-} f (x) - l i m x \to c^{+} f (x) ∣ ∣ ∣$
= |b - a|

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if f(x) is discontinuous at x = c, and have a jump at x = c then the value of jump is -

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if f(x) is discontinuous at x = c, and have a jump at x = c then the value of jump is -

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. If

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For

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Let f(x) ={ax>cbx≥c} :a,b,cϵ−R if f(x) is discontinuous at x = c, and have a jump at x = c then the value of jump is -undefined

It is given that the function is discontinuous at x = c, the jump will be nothing but the difference (modulus) of ∣∣∣limx→c−f(x)−limx→c+f(x)∣∣∣ = |b - a|

Let f(x) = ${\begin{matrix} a & x > c b & x \geq c \end{matrix}} : a, b, c ϵ - R$
if f(x) is discontinuous at x = c, and have a jump at x = c then the value of jump is -
undefined

It is given that the function is discontinuous at x = c, the jump will be nothing but the difference (modulus) of $∣ ∣ ∣ l i m x \to c^{-} f (x) - l i m x \to c^{+} f (x) ∣ ∣ ∣$
= |b - a|