For what values of x is g continuous? g(x)=⎩⎨⎧​0xx=0​ if x is rational if x is irrational ​x∈Rx=1x=−1​ -/0.71 Points] S

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For What Values Of X Is G Continuous G X 0xx 0 If X Is Rational If X Is Irrational X Rx 1x 1 0 71 Points S 1 (89.8 KiB) Viewed 40 times

For what values of x is g continuous? g(x)=⎩⎨⎧​0xx=0​ if x is rational  if x is irrational ​x∈Rx=1x=−1​ -/0.71 Points] SCALCET9 2.5.001. Write an equation that expresses the fact that a function f is continuous at the number 7. limx→7​f(x)=f(7)limx→7​f(7)=f(x)limx→7+​f(7)=limx→7−​f(7)lim7→x​f(x)=f(7)lim7→x​f(7)=f(x)​
If f is continuous on (−∞,∞), what can you say about its graph? (Select all that apply.) The graph of f has a hole. The graph of f has a jump. The graph of f has a vertical asymptote. none of these
Sketch the graph of a function f that is defined on 1R and continuous except for the stated discontinuities. jump discontinuity at 9 , removable discontinuity at 7
Use continuity to evaluate the limit. θ→3π/2lim​sin(tan(cos(θ))) SCALCET9 2.5.026. Consider the following function. f(x)=x−8x2−17x+72​ (a) Explain why f has a removable discontinuity at x=8. (Select all that apply.) f(8) and x→8lim​f(x) are finite, but are not equal. f(8) is undefined. x→8lim​f(x) does not exists. x→8lim​f(x) is finite. none of the above (b) Redefine f(8) so that f is continuous at x=8 (and thus the discontinuity is "removed"). f(8)=
(a) f(x)=x−1xn−1​,a=1 The discontinuity is removable. The discontinuity is nat removable. g(x)= (b) f(x)=x−7x3−x2−42x​,a=7 The discontinuity is removable. The discontinuity is not removable. g(x)= (c) f(x)=[sin(x)], a =x (Recall that [n(x)] means the largest integer that is less than or equal to n(x).) The discontinuity is remavable. The discontinuity is not removable. g(x)=