Select all boards below on which the formula Vx Big(x) → 3y Circle(y) ^ Aligned(x,y) is true. Hint: remember that any piece is aligned with itself. OF

Q: Suppose at x = x, Vf(x) = 0. What can you say about x if (a) f(x) is convex? (b) f(x) is concave?…

A: In multivariable calculus ∇f is similar to df/dx of single variable calculus & the ∇²f is…

Q: Find the points on the cone z² = x² + y² that are closest to the point (-5,4,0)

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Q: Find c > 0 such that the area of the region enclosed by the parabolas y = x² – c and y = c² – a² is…

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Q: Y is the midpoint of XZ and V is the midpoint of WZ. If VY = 32, what is WX? WX Submit

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Q: Find the greatest and smallest values that the function f(x, y) = 4x+5y takes on the circle x2 + y?…

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Q: The axis of symmetry of the cylinder is parallel to the z-axis. х-ахis. O y-axis.

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Q: Use the trapezoidal rule with n = 5to estimate V7 + y³dy

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Q: Find the points on the cone z = x+y' that are closest to the point (-2,3,0) 22

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Q: Consider the solid that is bounded above by x² + y? + z? = 169 and below by z=5. %3D

A: In this question, we have to write the triple integral to find the volume of the solid bounded by…

Q: Use the Trapezoidal Rule with n=6 to approximate π∫0sin2xdx.

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Q: dr Consider the integral I- composite Trapezoidal rule with n-4 subintervals is: The approximation…

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Q: Among all rectangular boxes defined by the inequalities 0 ≤x ≤ a, 0 ≤ y ≤ b, 0 ≤ z ≤ 1, find the one…

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Q: Find the value(s) of c such that the area of the region bounded by the parabolae y = x² – c² and y =…

A: Given information:- Find the value(s) of c such that the area of the region bounded by the parabolae…

Q: use the trapezoidal rule to approximate use n=6 and h=1

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Q: Given the expression |z + 3 – 2i| =,Find the geometric region of space where the z exists in. Graph…

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Q: For what minimum integer value of a, will the line ax+(a+1) y =18 www (a> 0) have two intersection…

A: If the line cuts the circle at two points then given line is secant line of the circle .The…

Q: A surface in R³ is defined by the equation 4z = x² + 4y“.

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Q: Determine the convexity/concavity property of the following: (ii) f (x, y) = 2x² – y?

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Q: Evaluate [. 2y² + 4z² ds, where o is the first octant portion of a cone z = x² + y2 with height of…

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Q: The graph of g consists of two straight lines and a semicircle. Use it to evaluate each integral. y

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Q: Show that the function (x2+y2 t224이) is a Solution of Loplace's equation d2u dy?

A: It will be solution of given Laplace equation only when, it will satisfy it.

Q: Q3: Find the length of y=√x+2,1 ≤ x ≤ 7, Using ds = Y 04 1+²dy rotating

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Q: Please evaluate (3y – einl2) dr + (7x + V yt + 1) dy, where C is the circle x² + y² = 9. Hint: use…

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Q: (d) | (3+ecos (0 sd AX ·

A: As per your query the solution of the problem (a) has been done in midpoint rule. For the solution…

Q: 5. In the standard (x, y) coordinate plane, the midpoint of LM is at (4, –4) and L is at (1,3). What…

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Q: Ue langrange multipliars to fined the Shortest distancé fam the to the pGine x+g+Z=1. point (7,0,)

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Q: Use the method of undeterminad Coefficiento to slve the initial valene proalem : yo +Qy'+5y=cin…

A: The given initial value problem is              y''+2y'+5y=e-tsin(2t)  , y(0)=1, y'(0)=0 We find the…

Q: Find the Felative Maximum vasve of Fx,x) = x*- y, Subuicct to the Construint X-Y=24.

A: The given function is as follows. fx,y=x2-7y2 the given constraint is as follows. x-y=24y=x-24 The…

Q: Find the uolume of the region abave the メy- plane inside the cone xZ+y2 glirder and inside the…

A: Convert the parametric form.

Q: Find the points on the cone z 22 x2 + y? that are closest to the point (-5,2,0)

A: Aim: Find the points on the cone z² = x² + y2 that are closest to the point (-5,2,0).   Basic…

Q: O By using Green's theorem, evaluate $ (In (2²) + æy² – y²) dæ + (ev + x²y – 3ry) dy, where C is the…

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Q: Find the points on the cone z2 = x² + y² that are closest to the point (-2,2,0)

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Q: Evaluate f 3z2dz over C, where C is the upper half circle |z – connects points O and 1+i. -글히 %3D플…

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Q: For the qutegradsSEddy tringle Over the bounded by -0,4=0 and *+y=l-

A: We have to find the integral  ∬e2x+3y dx dy   over the region R bounded by curves: x=0, y=0, x+y=1

Q: Find the extreme values of z on the surface 2x² + 3y2 + z2 - 12xy + 4xz = 35.(DO NOT USE LAGRANGE…

A: For the solution follow the next steps.

Q: Find the points on the cone z 22 = x2 + y? that are closest to the point (-3,1,0)

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Q: consider the curue desoribed by 2y"-x²_4y vevity that the foint (4-25 les on this o8 wrE andd find…

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Q: 4. Evaluate where C is a circle of radius 2, parallel to the r - z plane and around the y-axis with…

A: Using the parametric equation of the curve C.

Q: Evaluate f.y ds where C is the upper half of circle x? +y² = 9, traversed in the counterclockwise…

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Q: Let R=[0,6]×[0,6]. Subdivide each side of R into m=n=3 subintervals, and use the Midpoint Rule to…

A: Given :  R=0,6×0,6m=n=3     MIDPOINT RULE:

Q: (2,2) b) Evaluate o x*y dx + x dy, shown in adjacent figure using green's theorem. where c is…

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Q: The solid inside the cylinder x² + y? = 4 that is above by the planes z = 3 – x and below by z = x –…

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Q: Use the method of Lagrange multipliers to maximize 2x + 3y – 4 on the circle x² + y? = 13

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Q: Find c > 0 such that the area of the region enclosed by the parabolas y = 390. c and y = c² – a? is…

A: we know that areaA of the region enclosed by given parabola is given by A=2∫-ccc2-x2dx=4∫0cc2-x2dx…

Q: Find the Võlumé of thé šólid generated by revolving the shaded region about the given axi About the…

A: Explanation: If we rotate the shaded region about the x-axis, we will get the cone shape. Height of…

Q: find the valume 9tntrat ed by y= X? on [0,31 rotating abaut thlina X-5.(shell melthod) rated

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Q: Show that the subtangent to y = x' at x = a is equal to a/3.

A: Definition used -                            Length of subtangent =ydxdy