8) Evaluate F dr where F(r, y, z) = (2yze2") i+ (ze2") j + (ye2") k and C is a curve with initial point r(0) = (2,1, 2) and final point r(1) = (0,2, 4). (Hint: Check if F is conservative first)

Q: Here is the contour plot of a differentiable function f. 2- (a) Evaluate f(2, 1). (b) Estimate fa(2,…

A: (a) Since the contour line which passes through point 2, 1 has a corresponding value 3. Therefore,…

Q: (5xy --- 6x(2^

A: Given,        F=(5xy-6x2)i+(2y-4x)j and   y=x3 from the point (1, 1) to (2, 8).

Q: Assume that F= (e^x−y)i+ (2y−x)j, C1 is curve from (0,1) to (2,5) along the graph of y=x^2+ 1, and…

A: Given , F=ex-yi^+ (2y-x)j^ C1 is a curve from (0,1) to (2,5) along the parabola y=x2+1 C2 is a line…

Q: along the following paths C:(a) x=2t^2, y=t, z=t^3 from t=0 to t=1; (b) the straight lines that A ·…

A: We will use parameterization to find line integral

Q: The equation of the tangent line to the graph of f(x) = Vx+1 At the indicated point (3,2) is:…

A: By using the derivative and slope intercept form required tangent equation is :

Q: Question 2 Find the minimum value of (x.y)=2xr+4y on the curve x^2+xy+y^2=16 Select one: а. -18 C b.…

A: Given, fx,y=2x+4yx2+xy+y2=16         let gx, ygx,y=x2+xy+y2-16

Q: 5. nts) Let F =, use Green's Theorem to evaluate F. dr where the curve C is C the curve shown in the…

A:

Q: Find the implicit equation of the tangent plane to z = e + x + x² + 12 at the point (6, 0, 55).

A: Given: z=ey+x+x2+12 Point (6,0,55)

Q: 5. What are the coordinates of the JNBS if J'(-2, 4), N'(3, 5), B'(2, 3), and S'(0, 2) after R(90".…

A: Given: J'(-2,4) , N'(3,5), B'(2,3) and S'(0,2)

Q: Find an equation of the tangent plane to the surface x² + 2y² + z² = 175 at the point (5, -5, 10). O…

A:

Q: 2. Solve for x: 63x+1 = 22x-3 Leave your answer in exact form

A: 63x+1=22x-3

Q: 3. If f is the function given by f(x) = -x³ + x² + 3x-2, name the open interval where the graph of f…

A:

Q: Find the indicated value for f(x,y) = x^2y^3  fxx(1,2) =  fyy(1,2) =  fxy(1,2) =  really…

A: Given query is to find indicated partial derivative.

Q: 7. F- dr from (0,0) to (3,9) along the curve y=x' if F(x, y, z) = 4 xyi + 3xy'j Evaluate

A:

Q: Let f(1,y) = (r+ay°,r²y°,2r + by), g(u, v,w) = (3u² + bv² + w°, uvw). Find the derivative of…

A: Let f(x, y)=x3+ay2, x2y3, 2x+by,  gu, v, w=3u2+bv2+w3, uvw. We need to find the derivative of fgu,…

Q: Encuentre máximo(s) y/o mínimo(s) relativos de f(x) = 1- 5z2 +4. (Si es que estos existen).…

A:

Q: Which of the following functions are linear? Justify your answer in a comprehensible manner. In the…

A:

Q: Evaluate F dr where F(x, y, z)= (x', y’, xyz) and C is the line segment from х, у, со (1, 4, 3).

A: Use parametric to solve