Unit P Quizzam Review Name__________________________________ You will also need to study the first quiz and homework from this unit!! 1. Consider the following function defined by it’s graph: . Find the following limits: a) lim!→#$% I(K) b) lim!→#$& I(K) c) lim!→#$ I(K) d) lim!→#' I(K) e) lim!→' I(K) 2. Graph the following piece-wise function. Then find the limits. x2 – 2x if x < 5 f(x) = 10 if x = 5 2x + 5 if x > 5 a) b) c) d) e) Solve the following limits algebraically. Show all necessary work! 3. lim!→#* !+,$-!,.*.*#!+ 4. lim!→/ !0#1!#2!0#.1 5. lim!→. !0#.!+,!#.!#. 6. lim!→#/ !+,1!,$.!0,*!+,1!,/

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xfx -®

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8

6

4

2

-2

-4

-6

-5 5

Solve graphically. 7. 8. 9. _____ Use trigonometry to solve the following. Show all work! 10. If the distance from a helicopter to a tower is 300 feet and the angle of depression is 40.2° , find the distance on the ground from a point directly below the helicopter to the tower.

11. The angle of elevation from a point 116 meters from the base of the Eiffel Tower to the top of the Tower is 68.9° . Find the approximate height of the tower. Graph the piece-wise function. Answer any questions following. 12. 13.

a. Find f(x) when x = 4. a. Find g(x) when x = -1. b. Find the limit as x approaches -1. b. Find the limit as x approaches -1. c. Find the limit as x approaches 0. c. Find the limit as x approaches -1+. d. Is there anywhere the limit DNE? d. Find the limit as x approaches 2.

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14. Draw a graph the satisfies the following conditions: lim!→#.% 7(9) = 0 lim!→. 7(9) = 1 lim!→'% 7(9) = 4 7(−5) = −4 15. Consider the following function: I(K) = √K − 4 + 2 a. Sketch a graph of the function. b. List any maximums/minimums. c. State the domain in interval notation. d. State the range in interval notation. e. How has this function been translated from the parent function?

1

Pre-Calculus HONORS Name: _________________________

PUSHED BEYOND THE LIMIT?

First, find the limits of each problem. Put the answers in order from least to greatest, using the letter corresponding with the problem. If a limit does not exist, it will go at the END. There are four that DNE…you must put them in order to spell the last word.

Using the graph above, Using the graph above,

E) E) O) R)

R) L) I) T)

N) E) M) H)

A) I) I) E)

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f x-®

=0

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lim ( )x

f x+®

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f x®

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lim ( )x

f x®-

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f x-®

=18lim ( )x

f x+®

=

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lim ( )xf x

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0lim ( )x

f x-®

=0

lim ( )x

f x+®

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4lim ( )x

f x+®

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lim ( )xf x

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12lim ( )x

f x+®-

=12

lim ( )x

f x-®-

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2

Using the graph to the left, find the limit of: T)

10lim ( )x

f x+®-

=

10lim ( )x

f x-®-

=

10lim ( )x

f x®-

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30lim ( )x

f x+®

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30lim ( )x

f x-®

=

40lim ( )x

f x®

=