Limits Cheat Sheet

Let f(x) = { x^2 - 9/ x -3 , x does not =3 3, x = 3​ Which of the following statements are true? I. lim f(x) exists x→3 II.f(3) exists III. f(x) is continuous at x=3

I and II only

* # 2 on Limits and Continuity Test. There is a graph on this problem. Use the graph of f(x) to evaluate the limit. lim f(x) = x→1

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*#4 on Limits and Continuity Test. There is a graph for the problem. Use the graph of f(x) to evaluate the limit. lim f(x) = x→2

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*There is a graph. lim f(x) = x→1 −

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Which of the following functions is not continuous for all real numbers x?

f(x) = 3/ (x+1)^4

lim ( | x-3 |)/ (x - 3) x→3−

-1

#13 on Limits and Continuity Test. There is a table. The function f is continuous on the closed interval [0,2] and has values given in the table above. The equation f(x) = 1/2 must have at least two solutions in the interval [0,2] if k =

0

*There is a graph for this problem. lim f(x) x→2

0

lim (sin(7x)/(x) x→0​

0

# 3 on Limit and Continuity Test. There is a graph. Use the graph of f(x) to evaluate the limit. lim f(x) = x→2​

1

Find lim f(x) where f(x) = { ( 7 - x, x < 4)(2, x=4)(pi/2+1, x > 4) x→4

3

lim (x^2 - 2x - 8) / (x^2-16) x→4

3/4

True or False: It is possible to tell if lim f(x) x→4 ​f(x) exists by only examining f(x) for x close to but greater than 4.

False

True or False: if lim f(x) x→a exists, then f(a) exists.

False

True or False: If you know in advance that lim f(x) exists x →4 , you can determine the value of the limit by knowing all the values of f(x) for all x > 4?

True

Find the the values of c so that the function f(x) = {( c^2 - x^2, x is < or equal to 3) ( x + c , x > 3)

c = -3, 4

*This is #10 on the Limits and Continuity test. There is a graph. Use the graph of f(x) above to determine which one of the following statements is true.

lim f(x) exists. x→1