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Is XSIN 1 x is differentiable?

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Is XSIN 1 x is differentiable?

Prove it is a differentiable function. x→0(xsin 1x ). x→0(xsin 1x )=0. (8) Therefore f(x) is differentiable at x=0 and f′(0) = 0.

Why is a function not differentiable at x 0?

The left limit does not equal the right limit, and therefore the limit of the difference quotient of f(x) = |x| at x = 0 does not exist. Thus the absolute value function is not differentiable at x = 0.

Does the function f/x )= XSIN 1 x have a removable discontinuity at x 0?

The function f(x)=xsin(1/x) is not 0 at x=0 as it is not even defined there. But it does have a removable discontinuity there, i.e. limx→0xsin(1/x)=0. You can easily prove this using Squeeze Theorem, comparing f(x) to |x| because |sin(1/x)|≤1.

Is the function XSIN 1 x continuous?

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2 Answers. It is not continuous at 0 .

How do you prove a function is not differentiable at a point?

If a graph has a sharp corner at a point, then the function is not differentiable at that point. If a graph has a break at a point, then the function is not differentiable at that point. If a graph has a vertical tangent line at a point, then the function is not differentiable at that point.

What is the derivative of 1 x?

-1/x2
Answer: The derivative of 1/x is -1/x2.

How do you check a function is differentiable or not?

A function is formally considered differentiable if its derivative exists at each point in its domain, but what does this mean? It means that a function is differentiable everywhere its derivative is defined. So, as long as you can evaluate the derivative at every point on the curve, the function is differentiable.

How can a function fail to be differentiable?

How can a function fail to be differentiable?

  1. The function may have a discontinuity, e.g., the function below at x=−1.
  2. The function may have a sharp change in direction, e.g., f(x)=|x| at x=0.
  3. The function may have a vertical tangent, e.g., f(x)=x1/3 at x=0.
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Is XSIN 1 x continuous function?

The function x sin(1/x) is obviously continuous except when x = 0 where it is not defined. The given function is x sin(1/x) for non-zero x and 0 when x = 0; this function is continuous for all x.

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