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).)
Answer:
The constant in the algebraic expression to represent the pattern below is 4.
Step-by-step explanation:
Imortant Tip:
Given the pattern
computing the differences of all the adjacent terms
The difference between all the adjacent terms of the pattern is the same which is
Hence, the given pattern represents the Arithmetic sequence.
Therefore, the constant in the algebraic expression to represent the pattern below is 4.
