Question 22 130 Chapter 2 Limits and DerivativesDetermine the limits in Problems 16 to 24. If the limitexists, explain how you found the limit. If the limit doesnot exist, explain why.28. Consider the statement lim x2= 4. How close doesx→2x need to be to 2 to ensure that x² is within the givendistance of 4?116. lim –|x +3|а. 0.1b. 0.01с. 0.00117. limx→-3+ x +3x→5 x29. Consider the statement lim /x = 0. How closex→0+18. lim cOs x19. lim cos(7 x)does x need to be to 0 to ensure that /x is withinx→-1X→-1the given distance of 0?Vx +2 – 2In x20. limх1 х — 121. limа. 0.1b. 0.01с. 0.001x→2х — 230. Consider the statement lim In x = 1. How close doesXex223. limx→0 xx need to be to e to ensure that In x= 1 is within the22. limx→0 xgiven distance of 1?(x – 4)²а. 0.1b. 0.01с. 0.001-24. limx→4 |x – 4||31. Consider the function-25. Consider the functionV4 – x2 – 2f(x) =x2f (x) = /x cosa. Use technology to graph y = f(x) over the inter-val [-2, 2].b. Use technology to graph yterval [-0.1, 0.1]. Based on your graph, guess thevalue of lim f(x).whose graph is given Figure 2.31. Does lim f(x)f(x) over the in-x→0+exist? If so, what is it? If not, why not?x→0c. Use technology to graph y = f(x) over the inter-val [-10-7, 10–7]. Based on your graph, guess thevalue of lim f(x).0.20.20,40,6x→0d. Most technologies can keep track of sixteen orfewer digits. In light of this observation, discusswhat might be happening in parts b and c.-0.2--0.4In(1+x²)32. Consider the function f (x)()Figure 2.31 Graph of the function f(x) = x cosx2a. Use technology to graph yval [-2, 2].f(x) over the inter-26. Consider the function

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Question 22 130 Chapter 2 Limits and DerivativesDetermine the limits in Problems 16 to 24. If the limitexists, explain how you found the limit. If the limit doesnot exist, explain why.28. Consider the statement lim x2= 4. How close doesx→2x need to be to 2 to ensure that x² is within the givendistance of 4?116. lim –|x +3|а. 0.1b. 0.01с. 0.00117. limx→-3+ x +3x→5 x29. Consider the statement lim /x = 0. How closex→0+18. lim cOs x19. lim cos(7 x)does x need to be to 0 to ensure that /x is withinx→-1X→-1the given distance of 0?Vx +2 – 2In x20. limх>1 х — 121. limа. 0.1b. 0.01с. 0.001x→2х — 230. Consider the statement lim In x = 1. How close doesX>ex223. limx→0 xx need to be to e to ensure that In x= 1 is within the22. limx→0 xgiven distance of 1?(x – 4)²а. 0.1b. 0.01с. 0.001-24. limx→4 |x – 4||31. Consider the function-25. Consider the functionV4 – x2 – 2f(x) =x2f (x) = /x cosa. Use technology to graph y = f(x) over the inter-val [-2, 2].b. Use technology to graph yterval [-0.1, 0.1]. Based on your graph, guess thevalue of lim f(x).whose graph is given Figure 2.31. Does lim f(x)f(x) over the in-x→0+exist? If so, what is it? If not, why not?x→0c. Use technology to graph y = f(x) over the inter-val [-10-7, 10–7]. Based on your graph, guess thevalue of lim f(x).0.20.20,40,6x→0d. Most technologies can keep track of sixteen orfewer digits. In light of this observation, discusswhat might be happening in parts b and c.-0.2--0.4In(1+x²)32. Consider the function f (x)()Figure 2.31 Graph of the function f(x) = x cosx2a. Use technology to graph yval [-2, 2].f(x) over the inter-26. Consider the function

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22. lim x-0 |x|