Given the function f(x) with the following conditions:
We need to determine the value of \(f(f(f(a)))=21.\)
First, let's break it down step by step:
Now, we solve for a such that \(f(f(f(a)))=21.\)
Thus, the only solution that works is for a=12.
Now, let's compute the limit:
\(\lim_{x \to 12} f(x) = f(12) = 2 \times 12 = 24\)
So, the correct answer is 144.
Let \( y = f(x) \) be the solution of the differential equation
\[ \frac{dy}{dx} + 3y \tan^2 x + 3y = \sec^2 x \]
such that \( f(0) = \frac{e^3}{3} + 1 \), then \( f\left( \frac{\pi}{4} \right) \) is equal to:
Find the IUPAC name of the compound.
If \( \lim_{x \to 0} \left( \frac{\tan x}{x} \right)^{\frac{1}{x^2}} = p \), then \( 96 \ln p \) is: 32