Answer:
√3/2
Explanation:
The directional derivative at the given point is gotten using the formula;
∇f(x,y)•u where u is the unit vector in that direction.
∇f(x,y) = f/x i + f/y j
Given the function f(x, y) = y cos(xy),
f/x = -y²sin(xy) and
f/y = -xysin(xy)+cos(xy)
∇f(x,y) = -y²sin(xy) i + (cos(xy)-xysin(xy)) j
∇f(x,y) at (0,1) will give;
∇f(0,1) = -0sin0 i + cos0j
∇f(0,1) = 0i+j
The unit vector in the direction of angle θ is given as u = cosθ i + sinθ j
u = cos(π/3)i+ sin(π/3)j
u = 1/2 i + √3/2 j
Taking the dot product of both vectors;
∇f(x,y)•u = (0i+j)•(1/2 i + √3/2 j)
Note that i.i = j.j = 1 and i.j = 0
∇f(x,y)•u = 0 + √3/2
∇f(x,y)•u = √3/2
When we ask you the domain of f, you need to search for a forbidden value ?
for example you can't divide by zero, so assume x was equal to seven.
Then you would have f(7) = 7 / 7-7 = 7 / 0 this would be impossible because you can't divide by zero, yes ?
Other than that everything works, so the answer is c : all real values of x such that x ≠ 7
Good Luck
Answer:
4 3/5
Step-by-step explanation:
you first do 1 plus 3 which equals 4 then do 2/5 plus 1/5 which equals 3/5
The answer is A with the slope being 3/2 and the y intercept being -5.
