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**

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