Answer:

Step-by-step explanation:
Simply use the fact that the change in x squared + the change in y squared = the distance squared. (The Pythagorean Theorem)
1^2 + 4^2 = d^2
1 + 16 = d^2
17 = d^2
d = √17
Hope it helps :)
The equation of the tangent line at x=1 can be written in point-slope form as
... L(x) = f'(1)(x -1) +f(1)
The derivative is ...
... f'(x) = 4x^3 +4x
so the slope of the tangent line is f'(1) = 4+4 = 8.
The value of the function at x=1 is
... f(1) = 1^4 +2·1^2 = 3
So, your linearization is ...
... L(x) = 8(x -1) +3
or
... L(x) = 8x -5
You're just going to take exponents of 4. For example, 4 to the power of 1, 4 to the power of 2, 4 to the power of 3, and so on. To get the powers of 4, just multiply 4 by how much the exponent reads. For example 4 to the power of 3 is just 4 multiplied by itself 3 times.
4^1=4
4^2=16
4^3=64
4^4=256
4^5=1024
However, 1024 is greater than 1000 so we do not include it.
Answer:
y=-3
Step-by-step explanation:
I hope this works