Determine the differential eqn. of the ff. family of curves: a.) Straight lines with slope half the value of the x-intercept b.) Circles with center on the y-axis c.) Circles with center on the line y = x, and passing through the origin

Q: Find an equation of the tangent plane to the surface at the given point. g(x, y) = arctan 2, (2, 0,…

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Q: Sketch the graphs of the following cylinders. Properly identify a cross-section on the appropriate…

A: Given: Let's consider the given equation and graph the following cylinders. y=2x-4

Q: Consider the curve defined by z² = e²-v for z>0. At what value of z does the curve have a horizontal…

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Q: Find an equation of the tangent plane to the surface g(x, y) = x2 + y2, at the given point (1, −1,…

A: We have given the surface; g(x, y) = x2 + y2 and the point (1, −1, 2)

Q: Find an equation of the tangent plane to the surface at the given point. h(x, y) = In Vx2 + y?, (6,…

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Q: Find an equation of the tangent plane and a normal line to the surface z = In Vx2 + y2 at the point…

A: Given that: z=lnx2+y2

Q: 3. Find the equation of the tangent plane and normal to the surface z =x? +y? + 4 at point (1, -1,…

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Q: Find an equation of the tangent plane to the surface at the given point. g(x, y) = arctan L, , (3,…

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Q: Find an equation of the tangent plane to the surface f(x, y) = x2y at the given point (2, 1, 4) and…

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Q: Find an equation of the tangent plane to the surface at the given point. h(x, y) = In Vx2 + y², (6,…

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Q: Find an equation of the tangent plane to the surface at the given point. h(x, y) = In Vx2+ y², (12,…

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Q: Find for the equations for tangent plane and normal line at P,on the given surface 2 х2 — 3ху —у? -2…

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Q: 2. Explore the asteroid given by the parameterization 1). Šketch its graph, determine the slope of…

A: Use a line integral to find the area of the region enclosed by the asteroid…

Q: Find the angle of inclination of the tangent plane to the surface 2xy − z3 = 0, at the given point…

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Q: Find an equation for the tangent plane to the surface z = 4xy® + sin(rx) at the point (1, 1, 4)

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Q: Find the equation for the tangent plane to the surface at the indicated point. (Hint: Solve for z in…

A: Let's find.

Q: Find an equation of the tangent plane to the surface at the given point. h(x, y) = In Vx2 + y²,…

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Q: Find an equation of the tangent plane to the surface at the given point. g(x, y) = arctan Y, (6, 0,…

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Q: Find the tangent line(s) to the parametric curve given by a = t5 – 4t3 y = t? at (0, 4).

A: Find the tangent line(s) to the parametric curve given by x = t^5-4t^3 , y = t^2 at (0,4).

Q: Find an equation of the tangent plane to the surface at the given point. h(x, y) = In Vx? + y², (6,…

A: here h(x, y)=z then We can represent the function in the phoneF(x,y,z)=0 where F(x,y,z)=z−ln(x2+y2)…

Q: Find an equation for the tangent plane to the surface 4xy6 + sin(rx) Z = at the point (1, 1, 4)

A: We have to find the tangent plane  of z=4xy^6+sin(πx) at (1,1,4)  Find the partial derivative with…

Q: Find the slo pe of the Para bola y=X at the Point PC2,4).write an equation for the tangent to the…

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Q: b) Find equations for the tangent plane and normal line at the point P-(2, –3,18) on the surface…

A: x2+y-2xy-x+3y-z=-7   Let fx,y,z=x2+y-2xy-x+3y-z+7 and the point is 2,-3,18 Now,…

Q: Find an equation of the tangent plane to the surface at the given point. h(x, y) = In Vx2+ y², (3,…

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Q: Determine the intersection point of the lines tangent to the curve r (t) = (senπt, 2senπt, cosπt) at…

A: The given curve is rt=sinπt,2sinπt,cosπt. Differentiating it with respect to t:…

Q: Find an equation of the tangent plane to the surface at the given point. h(x, y) = In√√x² + y2, (3,…

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Q: The parametric curve x(t)=t−2t6 and y(t)=t7+2t2 is given. In which case is the tangent line at the…

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Q: Find an equation of the tangent plane to the surface y ln xz2 = 2, at the given point (e, 2, 1) and…

A: Given: ylnxz2=2 at the given point e,2,1

Q: Consider the following. x = sinh(t), y = cosh(t) (a) Eliminate the parameter to find a Cartesian…

A: Solution: The objective is to eliminate the parameter to find a Cartesian equation of the curve

Q: (a) Obtain the equation of the tangent plane and the condition for tangency to the conicoid Ar? +…

A: Conicoid given is- Ax2+By2+cz2=1 at the point (α,β,γ) We have to obtain the equation of the tangent…

Q: x² = y + 3y.

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Q: Find an equation of the tangent plane to the surface at the given point. h(x, y) = In Vx2 + y²,…

A: We have to find the equation of tangent plane

Q: Find the length of the subtangent and sub-normal at a point of the curve X y= bsin a

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Q: Find an equation of the tangent plane to the surface at the given point. g(x, y) = arctan y/x ,…

A: Find an equation of the tangent plane to the surface at the given point. g(x, y) = arctan(y/x).…

Q: Find an equation of the tangent plane to the surface at the given point. h(x, y) = In Vx2 + y², (12,…

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Q: Find an equation of the tangent plane to the surface at the give h(x, y) = In √x² + y², (12, 16, In…

A: we have to find tangent plane

Q: Find the equation for (a) the tangent plane and (b) the normal line at the point Po(8,0,8) on the…

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Q: Find an equation of the tangent plane to the surface at the given point. g(x, y) = arctan 2, (4, 0,…

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Q: Find an equation of the tangent plane to the surface at the given point. g(x, y) = arctan 2, (1, 0,…

A: This question is based on finding equation of tangent plane of function having two variables at a…

Q: If x = 8cos3theta and y = 8sin3theta, find the total length of the curve swept out by the point…

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Q: Find an equation of the tangent plane to the surface at the given point. g(x, y) = = arctan 2, (9,…

A: Follow the procedure given below.

Q: Find an equation for the tangent plane to the surface z +4 = ry" cos(2) at the point (4, 1, 0).

A: Use the partial differentiation for finding the tangent plane.

Q: Find equations for (a) the tangent plane and (b) normal line at the point P, on the given surface 1)…

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Q: Find an equation of the tangent plane to the surface z = y? - x² at the point (-4,5,9).

A: Finding partial derivatives with respect to x and y for finding plane equation.

Q: Find the family of curves in the plane such that in each point P(x,y) of it, the intercept of its…

A: Write the equation of the tangent for the family of curves for any point P (x , y). Assume the slope…

Q: eliminate the parameter to find a cartesian equation of the curve x= sinh(t),  y= cosh(t)

A: x=sinht,  y=cosht

Q: Find an equation for the tangent plane and the normal line to the surface x? + 2y? – 3z² = 3, at the…

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Q: Find the equation of the tangent plane to the surface z = +y? at the point (2, –2, 5)

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