Identify and remove, if possible, discontinuities off(x)= f(x)=x^32x^2x+2 /(x2.)

Identify and remove, if possible, discontinuities off(x)=x^2+x12 /(x3).

Identify and remove, if possible, discontinuities off(x)= 3x / 1x1.

What islim x1

limx1+f(x)whenf(x)={ 3 , -5 less then equal to x< 1

2 , 1 less than equal to x less than equal to 5 }

Evaluatelim x2 limx2x^3+x^26x / x^24.

where does the limit of f(X) does not exist . Please show the graph

where is f(x) tends to infinity . graph

Supposelim x3 f(x) = lim(x) 3 from the negative side f(x)andlim x3+ coming from the positive side are not equal

Which statements are true aboutfatx= 3?

I

Ifis continuous atx= 3

II

IIThere is a jump in the graph offatx= 3.

III

IIIThere is a vertical asymptote in the graph offatx= 3.

Letf(x)={3xk,x<5

1+kx,x5}

What value of k would make f continuous at x = 5?

What kind of discontinuity doesf(x)= =sin(1/ x^24)have at x = 0?

What kind of discontinuity doesf(x) = { 2, -5 less than equal to 0

x^2 , 0

Use limits to determine iff(x)=tan(1 / x1)is continuous at x = 1.

What kind of discontinuity doesf(x)=e^x /x

f(x)=ex^ / xhave at x = 0?