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: 6. Where does the tangent line to r = at the point (1, 0, 1) intersect the y-z plane.

A: Given:

Q: Classify all level curves of f(x, y) = Vy² – x² and draw its contour map.

A:

Q: Compute F. dr for the oriented curve specified. F(x, y) = (4x2, xy), line segment from (0, 0) to (2,…

A:

Q: Tangent to the curve z2 = 2xy + x2 , z = 3 , at the point ( 1, 4, 3) %3|

A: For a surface of the form: f(x, y, z)=0, the equation of the tangent at x0, y0, z0 is defined as…

Q: 2. Evaluate f (x^²y³ − 2y)dx + (3x + x³y²)dy where is the curve given below oriented in clockwise…

A:

Q: Show that the parametric curve r(t)= , t [-1,1] is smooth and compute its lengh

A: The given parametric curve is: r(t)=t1+t2, 11+t2 ;          t∈-1, 1

Q: -3. 3) to the curve given by f(x) =

A:

Q: Suppose that the plane tangent to the surface z = f(x, y) at (-4, 2, 5) has equation z + 5x + 4y =…

A: From the equation of tangent, we can derive: z = -(7 + 5x + 4y) Hence,

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: 11. Algebraically find the x-coordinate of all points where the given function has a horizontal…

A: Given: y=2x3+3x2-36x+1, y=2x+13x-2 We know that if any curvey=fx have horizontal tangent then slopem…

Q: 6. Given f(x, y) = 2x³y=x²y³, a) find the directional derivative of f(x, y) at (1, 1) in the…

A:

Q: Prove that there no line through the point (0,1) is tangent to the graph of y = x*.

A:

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

A:

Q: Compute ∫C(2x+√y)ds, where Cis the curve from (0,0) to (2,4) along y=x^2.

A:

Q: a) y = x' – 9x?

A: Since you have asked multiple question, we will solve the first question for you. If youwant any…

Q: Formadifperentiat euation byetimpnatig from atitaryConstant the fottowpng Curve:o -2X y=Ae where A…

A:

Q: )مه و و ي (x2 + y?, y* + 4x) · dr (2,1) )هد0( )ه,(

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

Q: Find the length of the curve traced by r(t) = t^2 i + (((t^3)/3) + 2)j, for 0 ≤ t ≤ 1

A: The solution is given as