Graphing Calculators in Calculus - Gettysburg College

Gr a ph in g Ca lcu la t or s

in Ca lcu lu s

(Usin g a

TI-83/84 S e rie s

Get t ysbu r g College

Ca lcu la t or )

S u m m a ry o f Gra p h in g Ca lc u la to rs in Ca lc u lu s

You s h ou ld b e a b le t o p e r for m ea s ily a n d efficien t ly a ll of t h e follow in g t a s k s on you r in d ivid u a l

g r a p h in g ca lcu la t or :

1.

D o a r it h m e t ic ca lcu la t ion s .

2.

D e fin e a n d ev a lu a t e fu n ct ion s .

3.

G r a p h fu n ct ion s , a n d ch a n ge t h e vie w in g w in d ow in m e a n in gfu l w a ys .

4.

T r a ce t h e gr a p h of a fu n ct ion .

5.

F in d ze r os of a fu n ct ion .

6.

F in d in t e r s e ct ion p oin t s of t h e gr a p h s of t w o fu n ct ion s .

7.

M a k e a fu n ct ion t a b le fr om a for m u la .

8.

F in d m a xim a a n d m in im a of a fu n ct ion .

9.

F in d t h e d e r iva t ive of a fu n ct ion a t a p oin t , a n d gr a p h d e r iva t ive ove r a n in t e r va l.

10.

F in d t h e d e fin it e in t e gr a l of a fu n ct ion over a n in t e r va l (L H S /R H S ).

11.

G r a p h t h e s lop e fie ld of a d iffe r e n t ia l e q u a t ion , a n d s k e t ch a s olu t ion cu r v e .

8 -6 -0 4 d e f

#1: U s in g a

TI-83/84 S e ri e s Gra p h in g Ca lc u la to r

In t r odu ct ion

Gr a ph in g ca lcu la t or s a n d com pu t er gr a ph in g soft wa r e a r e in dispen sa ble t ools in st u dyin g a n d doin g

m a t h em a t ics. F or t h is cou r se you a r e re qu ire d t o h a ve a gr a ph in g ca lcu la t or a va ila ble t o you a t a ll

t im es du r in g cla ss, wh en doin g you r h om ewor k , a n d wh ile t a k in g exa m s. Alt h ou gh a n y ca lcu la t or fr om

t h e followin g list is a ccept a ble, we v e ry h i g h ly re c o m m e n d t h a t you u se a ca lcu la t or fr om t h e Te x a s

In s t ru m e n t s TI-83/84 ser ies.

Te x a s In s t ru m e n t s TI-81, TI-82, TI-83/84 ser ies, TI-85, TI-86, or TI-89

Ca sio fx/cfx-7000/9000 ser ies

Sh a r p E L-9000 ser ies

H ewlet t -P a ck a r d 48/49 ser ies

Cla ss dem on st r a t ion , in st r u ct ion , a n d discu ssion will a ll u t ilize a ca lcu la t or fr om t h e TI-83/84 ser ies.

Alt h ou gh t h e ot h er list ed ca lcu la t or s ca n per for m m ost of t he desir ed oper a t ion s, t h ose ca lcu la t or s m igh t

be m or e difficu lt t o u se on som e oper a t ion s t h a t a r e expect ed in t h e cou r se. H a n dou t s a r e a va ila ble for

a ll of t h e Te x a s In s t ru m e n t s ca lcu la t or s t h a t a r e list ed.

Th e pu r pose of h a n dou t #1 is t o gu ide you t h r ou gh lea r n in g h ow t o u se t h e ba sic ca lcu la t or fea t u r es

t h a t a r e n ot r ela t ed dir ect ly t o fu n ct ion s a n d gr a ph in g. You will t ype or key-pr ess t h e it em s in bo ld .

Keyboa r d La you t

Ta k e a few m om en t s t o becom e fa m ilia r wit h t h e la you t of t h e keyboa r d. Th e lower cen t r a l por t ion

h a s wh it e/gr a y keys for t h e n u m er ica l digit s. Ar it h m et ic oper a t ion blu e k eys a r e on t h e lower r igh t side.

Blu e/gr a y a rro w keys for m a n ova l on t h e t op r igh t . J u st a bove m ost keys a r e t wo a ddit ion a l la bels:

(1) A yellow la bel on t h e 83 (blu e la bel on t h e 84) wh ich you ca n a ccess by fir st pr essin g a n d

r elea sin g t h e 2n d key (yellow on 83, blu e on 84) on t h e t op left of t h e keyboa r d, a n d

(2) A gr een let t er or sym bol la bel wh ich you ca n a ccess by fir st pr essin g a n d r elea sin g t h e gr een

ALP HA

key on t h e t op left of t h e keyboa r d.

N ote: If you r scr een is bla n k wh en you pr ess t h e ON key in t h e lower left cor n er , pr ess a n d r elea se t h e

2n d k ey (yellow on 83, blu e on 84) on ce a n d t h en h old down t h e u p a rro w key t o in cr ea se t h e scr een

con t r a st u n t il you see som et h in g on t h e scr een . Use t h e 2n d a n d d o w n a rro w keys t o r edu ce t h e

con t r a st .

Ar it h m et ic Oper a t ion s

P r a ct ice t h e followin g ca lcu la t ion s a lon g wit h ot h er sim ila r ca lcu la t ion s of you r own design u n t il you

a r e com for t a ble a n d pr oficien t wit h ba sic a r it h m et ic ca lcu la t ion s. Aft er you t ype in ea ch ca lcu la t ion t o

be don e, pr ess t h e E N TE R key in t h e lower r igh t cor n er of t h e keyboa r d. Use t h e CLE AR , a rro w , a n d

DEL

(delet e) keys t o m a k e t ypin g cor r ect ion s. E n t er ea ch of t h e ca lcu la t ion s a s on e for m u la wit h ou t

br ea k in g t h e for m u la down in t o sim pler pieces.

5+7

3.6 ! 8.25

(Use t h e su bt r a ct ion key on t h e r igh t side, ju st a bove t h e a ddit ion key.)

4¡Á2

(Not e t h a t m u lt iplica t ion is displa yed on t h e scr een by t h e " * " sym bol.)

9¡Â4

(Not e t h a t division is displa yed on t h e scr een by t h e " / " sym bol.)

2^3

(Th e ^ key, ju st a bove t h e ¡Â key, is for expon en t s: 2 3 .)

-4 + 9

(Use t h e n ega t ion (-) key on bot t om r ow for n ega t ives, NOT t h e su bt r a ct ion key.)

3 ¡Á -6

(Use t h e n ega t ion key, NOT t h e su bt r a ct ion key.)

2+3¡Á4

(Wh er e a r e t h e im plied pa r en t h eses?)

(2+3)¡Á4

(P a r en t h esis keys a r e a bove t h e 8 a n d 9 keys.)

2¡Á3+4

(Aga in , wh er e a r e t h e im plied pa r en t h eses?)

2+3¡Â4

(Im plied pa r en t h eses?)

(2+3)¡Â4

(P a r en t h eses m u st be u sed t o ca lcu la t e

2¡Â3¡Á4

(Wh a t wou ld you en t er t o ca lcu la t e

.)

?)

Wh en in dou bt a bou t wh ich oper a t ion s a r e per for m ed fir st , eit h er t r y a sim ple sim ila r exa m ple or u se

pa r en t h eses t o cla r ify wh a t you in t en d. Wh a t sh ou ld you en t er t o ca lcu la t e

5

2

(3+4)

5

-1

(P r ess t h e 5 key fir st a n d t h en t h e x 2 key on m iddle left side.)

2

(P r ess 5 a n d t h en x -1 key on m iddle left .)

(Tr y ea ch t wice: fir st u se t h e ¡Â key, a n d t h en u se t h e x -1 key.)

?

%4

(P r ess 2n d key fir st , t h en x 2 key wit h yellow % la bel on 83 or blu e % la bel on 84.)

(A closin g pa r en t h esis is r ecom m en ded, bu t is n ot n ecessa r y.)

(In clu de t h e closin g pa r en t h esis.)

(Wh er e a r e pa r en t h eses? Is t h is r esu lt t h e sa m e a s t h e la st r esu lt ?)

B¡Â2

(To t ype B, pr ess 2n d key fir st a n d t h en ^ key wit h yellow/blu e la bel "B".)

2¡ÁB

2B

3%4

(Om it t h e ¡Á key on t h is a n d t h e n ext t h r ee exa m ples;

t h ese fou r exa m ples illu st r a t e "im plied" m u lt iplica t ion .)

2(3+4)

1/2B

(Is t h e r esu lt wh a t you expect ed?)

La st E n t r y

Type a ga in t h e ca lcu la t ion 2 ( 3 + 4 ) a n d pr ess t h e E N TE R k ey. Now pr ess t h e 2n d k ey a n d t h en

t h e E N TE R key wit h t h e yellow/blu e E N TR Y la bel a bove it . Not ice t h a t you r la st for m u la en t er ed

r ea ppea r s on t h e scr een for you t o m a k e ch a n ges. Use t h e a rro w keys t o ch a n ge t h e "3" t o a "5" in or der

t o com pu t e 2 ( 5 + 4 ). P r ess t h e E N TE R key a s u su a l t o ca r r y ou t t h e ca lcu la t ion .

E dit you r la st en t r y (2n d E N TR Y) a ga in by fir st pla cin g t h e fla sh in g r ect a n gu la r cu r sor over t h e digit

"5" (u se le ft a rro w key). P r ess t h e 2n d key a n d t h en t h e key wit h t h e yellow/blu e la bel IN S . You a r e

n ow in t h e "in ser t " m ode in st ea d of t h e "t ypeover " m ode. Not ice t h a t t h e cu r sor is a fla sh in g u n der lin e

r a t h er t h a n a r ect a n gle. P r ess t h e 3 k ey a n d n ot ice wh a t h a ppen s. Th en pr ess t h e 7 key. If you pr ess

a n a rro w k ey, t h e cu r sor goes ba ck t o t h e t ypeover m ode a s in dica t ed by t h e fla sh in g r ect a n gu la r

cu r sor . P r ess t h e E N TE R key. (Th e cu r sor does n ot h a ve t o be a t t h e en d of t h e for m u la .)

P r ess t h e la st en t r y key (2n d E N TR Y) sever a l t im es a n d n ot ice t h a t you cou ld a lso edit sever a l

for m u la s ba ck .

N ote: Sin ce we've becom e a wa r e of differ en t cu r sor st yles, wa t ch wh a t h a ppen s t o t h e cu r sor st yle wh en

you pr ess t h e 2n d k ey. P r ess t h e 2n d k ey a ga in a n d wa t ch . If you ever m ist a k en ly pr ess 2n d , you ca n

ca n cel by pr essin g 2n d a ga in . Look a t t h e cu r sor t o see wh et h er 2n d is a ct iva t ed.

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