Let f(x, y, z) = x + yz and let C be the line segment from P = (0, 0, 0) to (4, 5, 5). (a) Calculate f(r(t)) and ds = ||r' (t)|| dt for the parameterization r(t) = (4t, 5t, 5t) for 0 ≤ t ≤ 1. (Use symbolic notation and fractions where needed.) f(r(t)) = ds = (b) Evaluate f f(x, y, z) ds. (Use decimal notation. Give your answer to three decimal places.) [ = f(x, y, z) ds dt

Q: Letf :Z→Zbedefinedbyf(x)=x^2 +1,and letC ={1,2,3}. Find f (C), f ^−1(C), f ^−1(f (C)) and f (f…

A:

Q: Suppose f(x, y, z) = xyz + 2xy + 2² · Compute the following values -(2,8₁16) - (-2,-8, 16) (1,-1,0)…

A: We have to find functional value.

Q: A solid concrete porch consists of 3 steps and a landing. The steps have a tread of 11 inches, a…

A:

Q: f (x, y) ~ bo + b1,0(x − 1)+b0,1(y−2)+ b2,0 (x - 1)² + b₁,1(x − 1)(y-2) + bo,2(y − 2)² +…...

A: We find the Taylor series of the given function

Q: 2. Sketch the domain of the following functions: a) f(x, y) = b) f(x, y, z)= 2-x-y - eª %2 In(4-x² -…

A:

Q: W(s, t) = F(u(s, t), v(s, t)), where F, u, and u are differentiable. If u(-6,0) = 6, u,(-6,0) = -2,…

A:

Q: Determine the interval(s) over which f(x) = (x − 4)³ is concave downward. O a O b Od (-∞0, 4) (-∞,…

A:

Q: Suppose z = f(x, y), where f is differentiable, x = g(t), and y = h(t). If g(6) = −4, g'(6) = −8,…

A: Step 1: Given that z=f(x,y),x=g(t),y=h(t) and…

Q: Letf (x, z) = 3x² – 12x + 3z² – In(z). Find the value of x* and z* where a min/max will occur. x*=2,…

A:

Q: f (x) = x 2 satisfies the Horizontal Line Test on the domain {x : x > O}.

A: Horizontal line test is a test used to find the function is injective that is one-to-one. First…

Q: the degree of homogeneity, if there is one, for eac 1 X1,X2, X3) = - xf +x +x X2 X3 O gro finotion:…

A: Introduction: For a function f(x,y), the degree of homogeneity is an integer n such that,…

Q: What function should be used to minimize the distance between y = x + 5 and the point (3, 1)? O D(æ)…

A: Explanation of the solution is given below...

Q: f : R --> R is defined by f(x) = 2x+1, A= (0,1)  and B = [ -1,1 ]    find f [A] and f-1[B]

A: