Choose the normal vector of the tangent plane to the surface defined by z =e4x²+16xy-9y2 at the point (-4, – 2,e92). O <- 64e156, – 28e156, 0> O None of the others ০ (-64e'56, -28e'56, - 1) O < 64e156, 28e156, 0> O <- 64e156, – 28e156, 1>

Q: Show that the directiona f(x, y, z) = z²x + y ² at ( X (1/15" + ) ; 255. them

A: fx,y,z=z2x+y3 P1,1,2v→=15i+25j We know directional derivative Dv→fP=∇fP.v→v→

Q: X 1 (A) If g tan , find the derivative 1² +2 yz of g at point (1,2,-1) in the direction of the…

A: Directional derivative of the function

Q: Find the points where the tangent is parallel to y=0. y=x*-8x°+22x2-24x+9 O E 0 (1,1),(2,2),(3,0) O…

A: Given: y=x4-8x3+22x2-24x+9 And y=0, represents the x-axis. The Power law: ddxxn=nxn-1

Q: Find the equation of the tangent plane to th surface 3x? + 5y? + 4z2 = 24 at the point (1, –1,2). 1.…

A:

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: 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: The equations zy? + 8xzcos(u) + ye" = 16 and r*yz+xe" – 5u²v² = 15 are solved for u and v as…

A:

Q: Plot the slope field of y=x+y using slopes m = -3, -2,-1,0, 1, 2. Sketch integral curves for…

A: First we plot the slope field and then plot the curve .

Q: Find the tangential and normal components.  r(t)=(t+1)i+2tj+t^ 2 × k     ,   t = 1

A: We'll answer the first question since the exact one wasn't specified. Please submit a new question…

Q: Compute F · dr where F(x, y) = and C is the path traced by the line segment starting at (0, −1) and…

A:

Q: Sketch the direction field of the DE y'=2x+y.  (Plot 9 or more points) Then sketch approximate…

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: Determine the equation of the normal line to the surface z2 cos(x + 2y) at the point (2, –1, 0).

A:

Q: Find equations of the tangent plane and normal line to the surface x = 5y² + 5z² — 28 at the point…

A:

Q: x^2y''-2xy'+2y=0; y1=x, y2=x^2 Verify that y1 and y2 are linearly independent

A: x^2y''-2xy'+2y=0; y1=x, y2=x^2 Verify that y1 and y2 are linearly independent

Q: What is the equation of the tangent plane to the graph of 3x²+4y²-2²=3 at the point (1,1,2) ? 03 1…

A:

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: Find the orthogonal trajectories of the family of curves y = kx'. = C (C) 3 y³ +x? = C (D) 3 y³ + 3…

A: Given y5=kx5 To find the orthogonal trajectory

Q: Find the x and y coordinates on the graph of f (x) = x³ - 3x where the tangent is horizontal. (A)…

A:

Q: Find the equation of the tangent plane to z= e" +x+x³ +1 the point (2, 0, 12).

A: Let a surface be represented by the function fx, y, z = c where c is a constant. Then the equation…

Q: Consider the graph of a folium of Descartes with equation 22³-190 -7-6-5-4-3-2 (a) Find the equation…

A: The graph of the equation is given.We have to find the equation of tangent line at the point and…

Q: The graph of y=x'-3x-24x +32 is concave upward on the interval (1, oo) because: O'=y"=0 Oy' is…

A: The given function is y=x3-3x2-24x+32