Recall the Maclaurin expansion for cos(x), valid for all real x :
Then replacing x with √5 x (I'm assuming you mean √5 times x, and not √(5x)) gives
The first 3 terms of the series are
and the general n-th term is as shown in the series.
In case you did mean cos(√(5x)), we would instead end up with
which amounts to replacing the x with √x in the expansion of cos(√5 x) :
Answer:
Step-by-step explanation:
So we have the system of equations:
And we want to multiply the first equation by some constant such that the resulting equation matches the coefficient of [x] in the second equation.
We can see that the coefficient of x in the second equation is 15.
So, to match 15, we must multiply the first equation by 3. So:
Multiply:
And we're done!