Question

kindaly first FIND THE LIMItS AND RANGEs THRough FOR thIS QUestion BY graphical methods AND BY HAND ON

NO OVERLaping , partial overlAPing ,COMPLETE oVerLAPING AND THEN AGAIN ZERO OR NO OVER LAPING .

Task 02: Compute (by both methods) and plot the response of the system 0 0 <t<1 x(t) = h(t)={1 1<t<2 0 2<t<10

Answer 1

3 2 (+)ht) oct<1 Ist ca 2 < t < 10 =) Here, given functim in a constant functie Hence, limit exists every where we just need to check the limits at t=2 lim LHL : lim alt) RHL lim alt) tit ---- ti RALLI Now, TIHL & RHLI Therefore, Limit does not exist at point te Again, THL a lim alt) RHL lim alt) t2 t2t. tyt t+2 RHL - 0 (HL fence LIHI & RHL Therefore, limit does not exist at point t=2

So for given domain Co, 10] the limit. exists everywhere except at point tot, t.ee The Range for given function of the system is the values of the limits i given domain i Range: 80,1% ter Graphical Methed xett) 2 - 2. 1 7 3 4 8 10 t The range of given function 2 nothing but projection of giver graph my-axls In our case, Range sot? Also, by looking graph we came to know that in giver domain (0,10] the graph exists. everywhere except at point t1't the value The value of limit for graph is o, 1 except at t=1 ft-2

They have given less than equal to and greater than equal to also Mathematically equal to must be for one side only. Due to that the thing happens is graph exist for X=2 at two points on Y axis. I have drawn graph as they have mentioned.

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