Question

Use the function and graph to answer the questions about existence, limits, and continuity. -x-3, -5?x<-4 x+5, -4<x<-2 3 -2<x<0 f(x) = 0, 0?x?1 2x-2, 1<x<3 2, x=3 -2x+10, 3<x<5 1, x=5 Does f(-3) exist? ? Yes ? No Does lim f(x) exist? x?-3 ? Yes ? No Does lim f(x) equal f(-3)? x?-3 ? No ? Yes Is the function continuous at x = -3? ? Yes ? No

          Use the function and graph to answer the questions about existence, limits, and continuity.
-x-3,  -5?x<-4
x+5,  -4<x<-2
3
-2<x<0
f(x) = 0,  0?x?1
2x-2,  1<x<3
2,  x=3
-2x+10, 3<x<5
1,  x=5
Does f(-3) exist?
? Yes
? No
Does lim f(x) exist?
x?-3
? Yes
? No
Does lim f(x) equal f(-3)?
x?-3
? No
? Yes
Is the function continuous at x = -3?
? Yes
? No

Use the function and graph to answer the questions about existence, limits, and continuity.
-x-3, -5?x<-4
x+5, -4<x<-2
3
-2<x<0
f(x) = 0, 0?x?1
2x-2, 1<x<3
2, x=3
-2x+10, 3<x<5
1, x=5
Does f(-3) exist?
? Yes
? No
Does lim f(x) exist?
x?-3
? Yes
? No
Does lim f(x) equal f(-3)?
x?-3
? No
? Yes
Is the function continuous at x = -3?
? Yes
? No

Added by Patricia T.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Vishal Parmar

06/16/2022

Step 1

Therefore, f(-3) exists and is equal to 0. Show more…

Show all steps

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Use the function and graph to answer the questions about existence, limits, and continuity. -x-3, -5≤x<-4 x+5, -4<x<-2 $\frac{3}{x}$, -2<x<0 f(x) = 0, 0≤x≤1 2x-2, 1<x<3 2, x=3 -2x+10, 3<x<5 1, x=5 Does f(-3) exist? Yes No Does $\lim_{x \to -3} f(x)$ exist? Yes No Does $\lim_{x \to -3} f(x)$ equal f(-3)? No Yes Is the function continuous at x = -3? Yes No