Question

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. 


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