Y-2x=6 => y=6+2x
Y+2x=0
(6+2x) + 2x = 0
6 + 4x = 0
4x= 6
X=6/4
X= 3/2
Y=6+2x
Y=6+2. 3/2
Y= 6 + 3
Y=9
Check: y-2x=6
9-2. 3/2 = 6
9 - 3 = 6
Answer: 9/7
Step-by-step explanation:
Recall that the derivative of a function f(x) at a point x = c is given by

By substituting h = x - c, we have the equivalent expression

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,

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

and cos(π/3) = 1/2.
For the second limit,

we observe that e²ˣ = 1 if x = 0. So this limit is the derivative of e²ˣ at x = 0. We have

and 2e⁰ = 2.