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Chapter 14: Q. 22 (page 876)

Use the graph shown to determine if the limit exists. If it does, find its value.

Short Answer

Expert verified

The limit does not exist.

Step by step solution

01

Step 1. Given Information  

We are given the graph and we need to determine if the limit exists and find its value.

02

Step 2. Finding the limit  

We need to find the limit of the function as xapproaches to 4of f(x).

The graph of the function reaches a removable discontinuity when xapproaches to 4from the left as well as whenxapproaches to2from the right.

From the graph, we can clearly see that fapproaches to 4from the left and to 2from the right as xapproaches to 4.

The value of the function from the left and right limits does not coincide.

Therefore, the limit does not exist.

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Most popular questions from this chapter

True or False For any function f, and any real number c,limx→c-f(x)=limx→c+f(x).

In Problem, graph each function. Use the graph to find the indicated limit, if it exists

limx→1f(x),f(x)=3xifx≤0x+1ifx>0

Graph each function. Use the graph to find the indicated limit, if it exists.

limx→π2f(x),f(x)=sinx

True or False Every polynomial function has a graph that can be traced without lifting pencil from paper.

In Problems 7– 42, find each limit algebraically.

limx→01-2x{"x":[[93,93,93,93,93,93,93,93,93,93,93,93,93,93,93],[115,115,115,115,115,115,115,115,115,115,115],[112],[112,112],[132,132,133,134,135,135,135,135,135,135,135,135,135,135,135,135,135,135,135,136,136,136,136,138,138,139,139,139,139,139,139,141,142,143,145,146,148,150,151,152,153,155,155,155,155,155,155,155,155,155,155,155,155,154,154,154,154,154,154,154,154,154,155,156,157,158,159,159,160,162,163,165,167,168,170,171,171,172,173,174,175,175,175,175,175,175,175,176,176],[90,91,91,95,98,100,103,104,106,107,107,107,107,107,106,105,104,104,104,104,104,104,104,104,104,104,104,104,104,104,104,104,104,105,106,106,107,108,110,111,113,115,115,117,118,119,118,116,113,111,109,106,105,103,103,102,101,101,101,101,102,104,105,107,109,111,111,113,114,115,115,116,118,119,119,120,121,122,123,123],[133,134,138,142,144,146,148,150,151,151,152,153,154,155,155,155,156,158,159,159,159,158,157,156,155,154,153,151,148,147,145,143,142,141,140,141,142,143,143,144,145,146,149,151,153,155,157,159,160,160,161,163,163,163,163,163,162,161,160,159,158,157,156,155,155,154,153],[182,182,182,182,182,182,182,182,182,182,182,182,182,182,182,182,182,182,182],[183,183,181,180,180,180,180,180,180,180,180,180,180,180,180,181,183,184,186,189,192,196,199,201,203,205,206,207,209,210,210,210,210,210,209,208,206,204,203,201,199,198,196,195,193,191,189,188,187,186,185,183,183],[212,213,215,219,223,225,228,230,231,233,234,234,235,235,235,235,234,231,231,229,228,227,227,227,227,227,227,227,227,227,227,227,227,227,229,231,237,250,261,273,287,295,302,313,320,327,337,340,343,347,348,351,353,355,356,357],[258,258,258,259,259,259,259,259,259,259,259,259,259,259,260],[298,304,310,316,319,321,325,327,328,329,330,331,331,331,332],[336,339,343,345,347,351,355,362,367,368,371,372,372,372,372,371,368,366,364,360,358,355,354,352,351,351,350,349,348,348,348,349,350,351,354,356,359,362,365,367,370,373,375,377,379,379,380,382,383],[383,384,386,388,390,391,393,395,395,396,396,396,396,396,396,396,396,396,396,396,396,396,396,396,395,394,393,392,391,391,391,391,391,391,392,393,394,395,397,399,400,402,403,404,405,406,405,404,403,403,402,401,399,397,396,395,395,394,393,392,392,392,392,392,392,393,395,396,397,398,399,402,403,403,404,405,406,407,407,408,409,410,411,411,412,413,414,415,415,416,417],[340,342,344,347,352,358,360,364,367,370,371,373,375,375,376,377,378,379,379,380,381,382,383,384,385,386,387,388,389,389,391,392,394,395,398,399,401,403,404,407,407,409,411,411,412,413,414]],"y":[[57.399993896484375,58.399993896484375,63.399993896484375,66.39999389648438,69.39999389648438,73.39999389648438,77.39999389648438,81.39999389648438,84.39999389648438,87.39999389648438,90.39999389648438,92.39999389648438,94.39999389648438,96.39999389648438,97.39999389648438],[81.39999389648438,83.39999389648438,85.39999389648438,90.39999389648438,93.39999389648438,97.39999389648438,99.39999389648438,101.39999389648438,104.39999389648438,105.39999389648438,106.39999389648438],[59.399993896484375],[59.399993896484375,59.399993896484375],[80.39999389648438,82.39999389648438,87.39999389648438,92.39999389648438,100.39999389648438,105.39999389648438,107.39999389648438,110.39999389648438,113.39999389648438,115.39999389648438,117.39999389648438,117.39999389648438,118.39999389648438,117.39999389648438,117.39999389648438,116.39999389648438,115.39999389648438,111.39999389648438,108.39999389648438,105.39999389648438,102.39999389648438,101.39999389648438,99.39999389648438,95.39999389648438,93.39999389648438,91.39999389648438,89.39999389648438,88.39999389648438,86.39999389648438,85.39999389648438,85.39999389648438,84.39999389648438,84.39999389648438,84.39999389648438,84.39999389648438,85.39999389648438,87.39999389648438,88.39999389648438,89.39999389648438,92.39999389648438,93.39999389648438,96.39999389648438,101.39999389648438,103.39999389648438,105.39999389648438,108.39999389648438,109.39999389648438,110.39999389648438,111.39999389648438,112.39999389648438,111.39999389648438,110.39999389648438,109.39999389648438,105.39999389648438,100.39999389648438,96.39999389648438,93.39999389648438,90.39999389648438,89.39999389648438,87.39999389648438,86.39999389648438,85.39999389648438,85.39999389648438,84.39999389648438,83.39999389648438,83.39999389648438,83.39999389648438,83.39999389648438,83.39999389648438,83.39999389648438,83.39999389648438,84.39999389648438,84.39999389648438,85.39999389648438,86.39999389648438,87.39999389648438,89.39999389648438,91.39999389648438,92.39999389648438,95.39999389648438,97.39999389648438,100.39999389648438,103.39999389648438,105.39999389648438,105.39999389648438,108.39999389648438,109.39999389648438,109.39999389648438,110.39999389648438],[136.39999389648438,136.39999389648438,136.39999389648438,138.39999389648438,140.39999389648438,143.39999389648438,146.39999389648438,149.39999389648438,150.39999389648438,153.39999389648438,156.39999389648438,159.39999389648438,161.39999389648438,162.39999389648438,164.39999389648438,166.39999389648438,167.39999389648438,168.39999389648438,16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