Question

5. Determine whether the following statements are TRUE or FALSE. If the statement is TRUE, then...

5. Determine whether the following statements are TRUE or FALSE. If the statement is TRUE, then explain your reasoning. If the statement is FALSE, then provide a counter-example. a) The amplitude of f(x)=−2cos(X- π/2) is -2 b) The period of g(x)=3tan(π/4 – 3x/4) is 4π/3.
 . c) If limx→a f (x) does not exist, and limx→a g(x) does not exist, then limx→a (f (x) + g(x)) does not exist. Hint: Perhaps consider the case where f and g are piece-wise defined at a. 
 . d) If f is continuous at a, then | f | is continuous at a. 
 . e) If |f| is continuous at a, then | f | is continuous at a. 


Homework Answers

Answer #1

(a)

we are given

we can compare with

A=-2

so,

amplitude =2

Hence, this is FALSE

(b)

we can compare with

now, we can find time period

Hence, this is TRUE

(c)

we can write

Hence, this is TRUE

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