Domain of function in interval notation

Calculus
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Aug 30th, 2015

Thank you for the opportunity to help you with your question!

a) F       answer is modulus of cos x

b)F         answer is √(x^2+3^2)

c)T

d)F          cannot divide denominator seperately

e)T

f)F           cannot divide denominator seperately

g)T          e^ ln x=x


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Aug 30th, 2015

How do you know how to check all of those questions 

Aug 30th, 2015

how do you know how to check each one of the question to see if they are true or not 

Aug 30th, 2015

they are evaluated by basic formulas.

which one you have doubt?

Aug 30th, 2015

All of them, what are the formulas 

Aug 30th, 2015

a) √(x^2) = modulus of x

b)√(x^2+9) =  √(x^2+3^2)  (this is not formula,9 = 3^2 

                                              we cannot simplify it further to modulus of x + 3

c) (7+a)/7 = 7/7 + a/7 

                 = 1 + a/7

d) x/ x+y

 we cannot split this denominator terms separately like numerator

  that is ,we cannot write this into x/x + x/y( as we done in the above problem,in the above problem we had separated the numerator terms which is allowed,but this is not the case with denominator)


Aug 30th, 2015

e) sin x= 2 sin (x/2 )cos (x/2)

   this is a basic formula ,so it is true

f) 2/ (4+x)

 this is similar case of question d

 we cannot separate denominator terms into 2/4  + 2/ x = 1/2 + 2/x

 so this solution is false

g)e^ ln x = x

  that is e^ ln ( of any number) = that number

  here   e^ ln 5/2 = 5/2

so it is true


Aug 30th, 2015

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