urgent help for this question

[kk243]

hey
 
so for the 2006 sample specialist exam 1, is the answer to the last question  c > or is it  c

im pretty sure its c

thanks in advanced

[kinslayer]

What is the question?

[kk243]

Find the values of c for which 5 tan –1 (x + 7) + c > 0 for all x.   

sorry for not giving the question 

[kinslayer]

Yeah just didn't know which sample exam it was.

The answer is , definitely. Arctangent has horizontal asymptotes at -pi/2 and pi/2, so for 5*arctan(x+7) they will be at -5pi/2 and 5pi/2. If you add 5pi/2 or more to that, the function will be strictly positive.

[kk243]

hmm i understand but does it matter if we use the greater than or equal to sign when the queston explicity uses the greater than sign?

[kinslayer]

hmm i understand but does it matter if we use the greater than or equal to sign when the queston explicity uses the greater than sign?

Yes. If you say that then you are excluding the possibility that .

Using a strict inequality does not introduce a contradiction, but it does not describe all possible values of and consequently it will cost you a mark.