Step-by-step explanation:
4 is the correct option...
M K is 12 I think ! I could be wrong
Recall that the derivative of a function f(x) at a point x = c is given by
![\displaystyle f'(c) = \lim_{x\to c} \frac{f(x) - f(c)}{x - c}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20f%27%28c%29%20%3D%20%5Clim_%7Bx%5Cto%20c%7D%20%5Cfrac%7Bf%28x%29%20-%20f%28c%29%7D%7Bx%20-%20c%7D)
By substituting h = x - c, we have the equivalent expression
![\displaystyle f'(c) = \lim_{h\to0} \frac{f(c+h) - f(c)}h](https://tex.z-dn.net/?f=%5Cdisplaystyle%20f%27%28c%29%20%3D%20%5Clim_%7Bh%5Cto0%7D%20%5Cfrac%7Bf%28c%2Bh%29%20-%20f%28c%29%7Dh)
since if x approaches c, then h = x - c approaches c - c = 0.
The two given limits strongly resemble what we have here, so it's just a matter of identifying the f(x) and c.
For the first limit,
![\displaystyle \lim_{h\to0} \frac{\sin\left(\frac\pi3 + h\right) - \frac{\sqrt3}2}h](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Clim_%7Bh%5Cto0%7D%20%5Cfrac%7B%5Csin%5Cleft%28%5Cfrac%5Cpi3%20%2B%20h%5Cright%29%20-%20%5Cfrac%7B%5Csqrt3%7D2%7Dh)
recall that sin(π/3) = √3/2. Then c = π/3 and f(x) = sin(x), and the limit is equal to the derivative of sin(x) at x = π/3. We have
![(\sin(x))' = \cos(x)](https://tex.z-dn.net/?f=%28%5Csin%28x%29%29%27%20%3D%20%5Ccos%28x%29)
and cos(π/3) = 1/2.
For the second limit,
![\displaystyle \lim_{a\to0} \frac{e^{2a} - 1}a](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Clim_%7Ba%5Cto0%7D%20%5Cfrac%7Be%5E%7B2a%7D%20-%201%7Da)
we observe that e²ˣ = 1 if x = 0. So this limit is the derivative of e²ˣ at x = 0. We have
![\left(e^{2x}\right)' = e^{2x} (2x)' = 2e^{2x}](https://tex.z-dn.net/?f=%5Cleft%28e%5E%7B2x%7D%5Cright%29%27%20%3D%20e%5E%7B2x%7D%20%282x%29%27%20%3D%202e%5E%7B2x%7D)
and 2e⁰ = 2.
Answer:
Genetics and Age
Step-by-step explanation:
The disease is hereditary meaning it gets passed down from past generations.