IIT JEE , AIEEE Forum - Mathematics , Differential Calculus

abhi_2cool

Q.) [ |sin

| + |cos

| ]

find the range of the given question.

AYUSHITANDON

its 1

mak graph of mod ,it ranges frm 1 to root 2

so greatst int is continuous and always eqal to 1

rate me plz

iitkgp_bipin

The expression inside the greatest integer function is periodic with period pi.

So, its enough to find the its variation from

=0 to

=pi

It varies from 1 to

2

Its greatest integer would be 1.

So the range is 1.

neeraj_agarwal_1990

U can add |sinx| and |cosx| graphically and find that function inside mod lies b/w 1 and root 2...so range is 1.

spideyunlimited

Let theta = x

as mod is there

func will behave in same way as if x was in first quadrant.

we get sin x + cosx

= root 2 . sin ( pi/4 + x )

diff. and equate to 0 find x for which value is max... we get root 2 as max

and for minimum value .. root2. sin ( pi/4 + x) and , so, sin( pi/4 + x) should be minimum...with x E [0 , pi/2]

draw graph of sin ( pi / 4 + x) by shifting graph of sinx to left by pi/4 units... and in interval of x E [0, pi/2] we see that minimum value is when x = 0

which gives minimum value as 1...

range is from 1 to root 2

f(x) E [1, root2]

NOW

when greatest integer function is applied..

we get range as

1

PLZ RATE :)

joyfrancis

well done spidey.

spideyunlimited

thanks joy *grey streaks* garnier.. take care
lol

pavan_puthr

The range is [-

2,

2].

tell me if im rite or rong. And do rate my reply............

abhi_2cool

thanx people.... specially spidey..... & bipin too....

ta d ans is 1......but spidey, i hav learnt 1 other method to solve d prob & i think its damn coooool.......

spideyunlimited

elaborate ur method

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