Question 14 Find the equation of the tangent plane to the surface y = 2x2 – (0,-1, –2) z2 at the point O y-2z 3 O y+ 4z = –9 O y+ 2z = -5 Oy-4z 7

Q: Question 25 Solve the problem. Write parametric equations for the tangent line to the curve of…

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Q: QUESTION 17 Let a , b and c be the last three digits of your student ID and let d=max(a,b,c). 2 How…

A: Given - Let a, b, c be the last three digits of your student ID and let d = max(a, b, c) To find -…

Q: QUESTION 7 Let P be the tangent plane to the surface z=x2+2y2 at the point Q=(-1,-1,3). Which of the…

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Q: x = t + t and y = t* + 2t²

A: If the parametric equation of a curve are x=f(t) and y=g(t), then the slope of the tangent line at…

Q: Find the line tangent to the right-hand hyperbola branch defined parametrically by x = sec t, y =…

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Q: y2 3. Find an equation of the tangent plane to the paraboloid x --= 1 at point (6, 2, 3). | a) x-y-z…

A: Equation of tangent plane

Q: Find parametric equations for the tangent line to the curve with the given parametric equations at…

A: The given curve is rt=t2+1,4t12,et2-t. Notice that the given curve satisfies t=1(If t=1 is plugged…

Q: Question 4 Evaluate fVdr which V given by V = xy + 2xy + yz between A(0,0,0) and B(2,1,3) along the…

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Q: Question 14 Solve the problem. Find the equation for the tangent plane to the surface z = 8x2 - Sy2…

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Q: Question 13 Solve the problem. Find parametric equations for the normal line to the surface x² +…

A: Find parametric equations for the normal line to the surface x2 + 2xyz + y2 = 4z2 at the point (1,…

Q: 12- Find an equation of the tangent plane to the given parametric surface at the specified point.…

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Q: Question 22 Question 4 (6 + 1+7+ 6 = 20 marks). Question 4 b) ii) - 6 marks Evaluate the line…

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Q: Question 3 Express the curve by an equation in r and y given r(t) = sec² (t) + 2 and y(t) = 5 +…

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Q: Find an equation of the plane tangent to the following surface at the given point. 5xy + 7yz + 6xz -…

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Q: 3. Let f(x, y) = xy+ y². Find the equation of the tangent line in parametric form in the x-direction…

A: Solve the following

Q: Find parametric equations for the tangent line to the curve with the given parametric equations at…

A: given parametric equations are x=1+12t , y=t3-t , z=t3+t

Q: Q2 - A) Find the parametric equations for the line that is tangent to the given curve : r(t) = (a…

A: To find The parametric equations for the line that is tangent to the given curve

Q: 10. Which of the following is the tangent line equation of the ellipse 9(x +y)² + (x – y)² = 36 at…

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Q: QUESTION 7 Let P be the tangent plane to the surface z=x2+2y2 at the point Q=(-1,-1,3). Which of the…

A: Given that  Z=x^2+2y^2  Point (-1,-1,3) To find teh point lies in p

Q: Question 16 Find the equation of the tangent plane to the given surface at the indicated point. x2…

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Q: A curve is given by the parametric equations x(t)=t2-4t and y(t)=t2+2t-3. The line tangent to the…

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Q: Question 19 Express the following parametrized curve by an algebraic equation in terms of x and y: x…

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Q: Question 1 Let f (x, y, z) = In (1+ x³ + y4 + 25) Find an equation for the tangent plane to the…

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Q: Consider the graph of r(t) = 2t^2i + t^2j + t^3 k Determine parametric equations of the tangent line…

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Q: QUESTION 2: Find equations of the Normal plane and Osculating plane of the y = 2t , x = 2 sin 3t , z…

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Q: Consider the surface S of equation 2 = x² + y*" An equation for the tangent line tangent to S at…

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Q: a)Find the equation of the tangent line to the curve and find a set of parametric equations for the…

A: To find the tangent equation of the line to the curve of intersection of both the given surfaces at…

Q: Find the length of the curve defined by the parametric equations y = 4 In((t/2)² – 1) from t = 9 to…

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Q: 2 Make a graph of the parametric equations x(t) = t - 3 on the interval 0sts 4 y(t) = ) = t ³ - 5 t

A: Given parametric equations  X(t) = t2-3  Y(t) =t3-5t

Q: Find parametric equations for the tangent line to the curve with the given parametric equations at…

A: Here, the given parametric equation of the curve is: r(t)=(x(t),y(t),z(t)) where x=6et, y=t e2t, z=t…

Q: 6. Locate all the points (if any) of the horizontal and vertical tangents to the curve defined by…

A: Consider the given equations,x=t2-t,y=t3-3tFind derivative with respect to…

Q: a)lim              (e^-x)(x^2+sinh(x+2))    x->∞   b) Find the point where the tangent to the…

A: find limit solve the parametric equation

Q: Question 12 Find a at time t = 1 for the plane curve r(t) = 4t²i+ 3tj. Round your answer to three…

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Q: QUESTION 14 The equation of the tangent plane to z=f(xy) =x² siny at the point (1,0,0) is given by…

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Q: (a) æ = sin t, y = csc t, 0 1. Thus, the curve is the portion of the hyperbola y = 1/x with y > 1.…

A: Given x=sin ty=csc t0<t<π2

Q: Which one of the following equations is the equation of the tangent plane to the surface xy + xz +…

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Q: The parametric equations for the line tangent to curve of intersection of the surfaces x? + y2 = 8 ,…

A: We have given the surfaces; And the point (2,2,8)

Q: QUESTION 3 Which of the following is an equation for the tangent plane to the surface z= xy at the…

A: Tangent palane ti the surface

Q: Question 19 Express the following parametrized curve by an algebraic equation in terms of x and y: x…

A: We have to find

Q: iven R'(t) = (4e²t, 2t ,2cosh t), and R(0) = (1, −2, 3), 1+t² find Ŕ(t), and give the parametric…

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Q: 1 '1+t²⁹ Given R'(t) = (4e²t, , 2cosh t), and R(0) = (1, -2,3).

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Q: QUESTION 7 The tangent plane to the graph of the surface z=In(x2+y2) at the point (1,0,0) contains…

A: To find the value of t

Q: 1-6 Find an equation of the tangent plane to the given surface at the specified point. 1. z = 3y² –…

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Q: Question 2 Find the length of the curves (a) r(t) = (2cost)i + (2sint)j + t*k, 0stS/4 (b) r(t) =…

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Q: Consider the equation of the surface S given by x2z2 + xy + yz = 7. An equation for the plane…

A: First differentiate at given point then use equation of tangent plane

Q: Question 1 Express the curve by an equation in x and y given x(t) = t² and y(t) = 5 tª + 1. a) Ox =…

A: x(t) = t2     -------- Equation (1) y(t) = 5t4 + 1 Now, y(t) = 5 (t2)2 + 1 y(t) = 5 x2 + 1  Where ;…

Q: Question 2 Consider the function f (x, y, z) = x² + y' – xyz Find the equation of the plane tangent…

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Q: A curve in the plane is defined parametrically by the equations written below. An equation of the…

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Q: Problem 5. Find an equation of the tangent plane to the surface z = In(2x + y) at the point (-1,…

A: The equation of a tangent of the surface F(x,y,z)=0 at the point (x0,y0,z0) is given by,

Coordinate Geometry

Coordinate geometry, also known as analytic geometry or Cartesian geometry in classical mathematics, is a type of geometry that is studied using a coordinate system. Coordinate geometry is a branch of mathematics that describes the position of points on a plane using an ordered pair of numbers called coordinates.