Determine the points at which the function f(x) is discontinuous. f(x) = {x - 7

Question

Determine the points at which the function f(x) is discontinuous. f(x) = {x - 7 / |x - 7| for x not equal to 7, 7 for x = 7. x = State the type of discontinuity. removable jump infinite none of these Determine the points on the interval [0, pi] at which the function is discontinuous. f(x) = 5 tan(2x) x = Classify these as removable, jump, or infinite discontinuities removable jump infinite The sawtooth function is defined by f(x) = x - [x], where [x] is the great integer function. Calculate the following limits. lim x rightarrow 2+ f(x) = lim x rightarrow 2- f(x) = At x = 2 the function is: right-continuous only left-continuous only continuous

Explanation / Answer

1.) Value of function at x= 7- is -1

Value at x = 7+ is 1

And value at x=7 is 7.

So, discontinuity is at 7.

It is jump discontinuity.

2.) It is discontinuous at x= -pi/4 and pi/4.

It is infinite discontinuity.

3.) x tends to 2+ is 0

Value at x tends to 2- is 1

Function is left continuous

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