Answer:
For we will have positive values only.
Rest are positive so will give positive values out of the modulus function.
Step-by-step explanation:
The absolute value of any number is its positive value only.
As for example and
both are having equal distance from
in a number line, one on the left other on the right side of the number line but are equidistant from
.
So absolute value of a number is its distance on number line from reference point .
One by one we will work with all of our question.
So we have to take the positive number out of the modulus function that is also called absolute value.
Assuming you mean f(t) = g(t) × h(t), notice that
f(t) = g(t) × h(t) = cos(t) sin(t) = 1/2 sin(2t)
Then the difference quotient of f is
Recall the angle sum identity for sine:
sin(x + y) = sin(x) cos(y) + cos(x) sin(y)
Then we can write the difference quotient as
or
(As a bonus, notice that as h approaches 0, we have (cos(2h) - 1)/(2h) → 0 and sin(2h)/(2h) → 1, so we recover the derivative of f(t) as cos(2t).)