Evaluating Limits

Oct 8, 2026

Evaluate each limit in a worksheet format from Infinite Precalculus. Problems present piecewise functions and expressions as x approaches specified values, including cases where a limit does not exist. Several items encourage using a provided graph to sketch the function before determining the limit. The set culminates in a critical thinking prompt requiring writing a custom piecewise function that matches given limit and value conditions at a target input.

LanguageEnglish

CategoryExam

FormatPDF

Pages4

Reading Time10 min

AccessFree to download

Evaluate each limit

Problems 1-10

Critical thinking question 11

Kuta Software-Infinite Precalculus Evaluating Limits Evaluate each limit. 1) 􀀖􀀎 f (x), f (x) = {􀀐xx􀀕􀀐􀀎􀀖􀀗, x 􀀐 􀀖 , x x 3) lim x􀁯 􀀐􀀕 f (x), f (x) = {􀀐􀀔􀀕x, 􀀐 􀀜 , xx 􀀟􀁴 􀀐􀀕􀀕 Name Date Period 􀁤 􀀖 􀀡 􀀖 2) lim x􀁯 􀀖 􀀐 􀀖 􀀐x 􀀎 􀀖 􀀐x 􀀎 􀀖 4) im􀁯 􀀕 f (x), f (x) = {􀀐 􀀕􀀔,, xx 􀁤􀀡 􀀕􀀕 Evaluate each limit. You may use the provided graph to sketch the function. 5) xm􀀐􀀔 􀀐 f (x), f (x) = { ~~ ~~ 􀀕􀀐, x 􀁤 􀀗 , x 􀀡 􀀐􀀔 􀀐􀀔 6) im􀁯 􀀐􀀕 f (x), f (x) = {􀀕􀀎 ,􀀎 􀀛 , x x 􀀟 􀀐􀀕 􀁴 􀀐􀀕 Evaluate each limit. 7) 9) lim x􀁯 􀀗 􀀐 lim x􀁯 􀀔 􀀎 f (x), f (x) = {􀀘􀀎 , x 􀀟 􀀗 x 􀁴 􀀗 f (x), f (x) = {x􀀐􀀐􀀗 􀀘, , x 􀀟 􀀔 x 􀁴 􀀔 8) 􀀖􀀐 f (x), f (x) = {x ,􀀗x 􀀐 10) lim x􀁯 􀀐􀀖 􀀐 f (x), f (x) = {􀀐 􀀐 􀀗x 􀀖 , x 􀀟 􀀖 x 􀁴 􀀖 􀀐 􀀗 , x 􀀟 􀀐􀀖 x 􀁴 􀀐􀀖 Critical thinking question: 11) Write a piecewise function where 􀀕 􀀐 f (x) 􀀠 􀀔 , lim x􀁯 􀀕 􀀎 f (x) 􀀠 􀀖 , and f (􀀕) 􀀠 􀀕 . Kuta Software-Infinite Precalculus Evaluating Limits Evaluate each limit. 1) 􀀖􀀎 f (x), f (x) = {􀀐xx􀀕􀀐􀀎􀀖􀀗, x 􀀐 􀀖 , 􀀓 x x 3) lim x􀁯 􀀐􀀕 f (x), f (x) = {􀀐􀀔􀀕x, 􀀐 􀀜 , xx 􀀟􀁴 􀀐􀀕􀀕 Does not exist. Name Date Period 􀁤 􀀖 􀀡 􀀖 2) lim x􀁯 􀀖 􀀐 􀀖 􀀐x 􀀎 􀀖 􀀐x 􀀎 􀀖 􀀖 4) im􀁯 􀀕 f (x), f (x) = {􀀐 􀀕􀀔,, xx 􀁤􀀡 􀀕􀀕 􀀐􀀖 Evaluate each limit. You may use the provided graph to sketch the function. 5) xm􀀐􀀔 􀀐 f (x), f (x) = { ~~ ~~ 􀀕􀀐, x 􀁤 􀀗 , x 􀀡 􀀔 􀀐􀀔 􀀐􀀔 6) im􀁯 􀀐􀀕 f (x), f (x) = {􀀕􀀎 ,􀀎 􀀛 , x x 􀀓 􀀟 􀀐􀀕 􀁴 􀀐􀀕 Evaluate each limit. 7) im􀁯 􀀗􀀐 f (x), f (x) = {􀀘􀀎 , x 􀀟 􀀗 x 􀁴 􀀗 􀀖 9) lim x􀁯 􀀔 􀀎 􀀐􀀖 f (x), f (x) = {x􀀐􀀐􀀗 􀀘, , x 􀀟 􀀔 x 􀁴 􀀔 8) lim x􀁯 􀀖 􀀐 􀀓 f (x), f (x) = {x ,􀀗x 􀀐 10) lim x􀁯 􀀐􀀖 􀀐 􀀐􀀔 f (x), f (x) = {􀀐 􀀐 􀀗x 􀀖 , x 􀀟 􀀖 x 􀁴 􀀖 􀀐 􀀗 , x 􀀟 􀀐􀀖 x 􀁴 􀀐􀀖 Critical thinking question: 11) Write a piecewise function where Many answers. Ex: f (x) = {xx, 􀀐 x 􀀎 lim x􀁯 􀀕 􀀐 f (x) 􀀠 􀀔 , 􀀔 , x 􀀟 􀀕 x 􀀠 􀀕􀀔 , x 􀀡 􀀕 lim x􀁯 􀀕 􀀎 f (x) 􀀠 􀀖 , and f (􀀕) 􀀠 􀀕 . Create your own worksheets like this one with Infinite Precalculus. Free trial available [at KutaSoftware.com](at KutaSoftware.com)

FAQs

What is the main task of the worksheet?

Evaluate each listed limit, often involving piecewise functions and approaching specific x-values.

How should you handle questions that mention a graph?

Use the provided graph to sketch the function so the limit as x approaches the given value can be determined.

What does the critical thinking question require?

Write a piecewise function that satisfies specified limit behavior as x approaches a value and the function’s value at a particular input.

Oct 8, 2026

Uploaded by MrHarris58