by eliminating the arbitrary constants "A" and "B" from the family of curves Ae³x y = + Be-7x O None y" – 4y – 21y = 0 O y' + 4y + 21y = 0 O y' + 4y – 21y = 0

Q: 7. Determine the coefficients a, b, c and d so that the curve y = ax* + bx³ + cx² + dx + e will pass…

A: Given a function of the curve, y=ax4+bx3+cx2+dx+e To find the coefficient a,b,c, and d such that the…

Q: Find an equation of the tangent plane to the surface at the given point. x2 + y2 + z2 = 21, (1, 4,…

A:

Q: 7. Find a single initial vahue problem that admits the family of solutions y = e and then find an…

A:

Q: 3. Determine the coefficients a, b, c, d that will make the curve y = ax³ + bx? + cx +d have…

A: We will find the value of a, b, c, and d as following .

Q: 4. Prove that the following curves are intersecting with a right angle: 5y-2x+y-xy= 0 2y+5x+x-x'y² =…

A: Find your answer below

Q: Calculate the are between curves defined by: x=y2+1 x=0 y=-1 y=2

A:

Q: Find the equations of the tangent line in the given plane. Tangent to the parabola z = x² + 3y² , x…

A: Tangent line equation problem....

Q: 6. Find the equation of the tangent plane to the surface: ==√√4-x²-2y², at (1,-1, 1)

A:

Q: FInd a so that the curve y = x3+ ax2+ 44 will have a relative extrema at (2,5). Find other extrema…

A: The given curve is y=x3+ax2+44. Since the curve has a relative extrema at (2,5), x=2 is a critical…

Q: 1. Find the are length of the curve x (+ 2)/2 from y=0 to y-1

A:

Q: Find a point on the curve y = x² that is closest to the point (18, 0). %3D AY y =2 (x, y) (18, 0)

A: Find a point on the curve y=x2 that is closest to the point  Here use distance formula…

Q: Given the curve y² = 5x – 1 at point ( 1,-2 ) , find the equation of tangent and normal to the…

A:

Q: Determine a, b, c and d so that the curve y = ax^3 + bx^2 + cx + d will have a critical point at the…

A:

Q: Find equations for the lines tangent and normal to the cissoid of Diocles y (4 – x) = 9x° at (2,6).

A:

Q: 2. A firm uses capital, K, and labor, L, to produce output P according to P = KaL, a, ß are positive…

A:

Q: #5. Find an equation of the tangent plane to the surface with the equation 12x z = x²y*. y at the…

A: The given equation of the surface: z=x2y4-12xy Therefore: f(x, y)=x2y4-12xy Now:…

Q: 1 1 from x=1 to x=3. 4x 3 5. Find the length of the curve given by y 3

A:

Q: (6) Find the points on the curve 5x2 + 6xy + 5y² = 9 which are nearest to and farthest from the…

A:

Q: Find an equation of the parabola y = ax2 + bx + c that passes through (0, 1) and is tangent to the…

A: Given" Parabola y = ax2 + bx + c that passes through (0, 1) and is tangent to the line y = x − 1 at…

Q: 4. Find the exact length of the curve. 36y2=(x²-4)3,2≤x≤3.y≥1

A:

Q: 2 35) Find a curve through the point (-4, 1) whose length integral, 1 s y s 2, is L = 1 +

A:

Q: Determine the constants c and d in the equation of the curve y = at (0, -1) and an inflection point…

A: This question can be solved using the concept of functions and derivatives.

Q: 7.Find the maximum and minimum distances from (0,0) to the curve 5x2+6xy+5y2=8

A:

Q: Let C be the curve y = x³ – 3x2 + 4x – 1 joining the points (1, 1) and (2, 3). Find the value of…

A: We need to find value of integral.

Q: Find the length of the curve parameterized by x = 2 + 3t² and y = 3 + 2t³ from t = 0 to t = 3.

A: To find the length of the curve parameterized by x=2+3t2 and y=3+2t3 from t=0 to t=3.

Q: 2. A firm uses capital, K, and labor, L, to produce output P according to P = KaL, a, 3 are positive…

A:

Q: 4. Evaluate S. y² – 3z + 2 ds for each of the following curve C is the line segment from (1,0,4) to…

A: We have ∫Cy2-3z+2 ds C is the line segment from 1,0,4 to 2,-1,1 Now, the parametric equation of the…

Q: 13. Find the length of the curve y4 + 8 from y = 1 to y = 4. X = 4y2

A: To find the length of given curve.

Q: If the equation of the tangent plane to x2+y²-83z2=0 at (1,1,/2/83) is x+ay+Bz+y=0, then a+ß+y=

A:

Q: FInd c and d so that the curve y = x3+ cx2+d will have a relative extrema at (2,5). Find other…

A: Given y=x3+cx2+d

Q: Find the points on the curve x2 + xy + y2 = 1 in the xy-plane that are nearest to and farthest from…

A:

Q: 4. Find the two values of a for which the line connecting the point (1, –1) to a point (a, a²) on…

A:

Q: 3/2 The length of the curve x= 4y2 from y=1 to y= 4 is given by

A:

Q: What is the equation of the curve y = ax* + bx + cx² + dx + e tangent to y = 25x (2,14), to y = 2x +…

A: By verifying options and substitution of point (-1,11) it is verifying option C

Q: 3x + xy? 2y + x?y dy dx

A:

Q: (1) Give two different parameterizations for each of the following curves. (a) The line segment from…

A:

Q: 4. Prove that the following curves are intersecting with a right angle: 5y-2x+y²-x²y = 0 2y +…

A:

Q: 1. Find the are length of the curve x = (y + 2)2 from y-0 to y=1

A: As per our guidelines we are supposed to answer only one question. Kindly repost other question as…

Q: Find the length of the curve defined by R(t) = (3t+1, 4t³/2, 4 - 3t²) from the point (1,0, 4) to (4,…

A: Given…

Q: determine the parametric coordinate of the critical point of the curve x=t^2+3t=2 and y=t^2-1.

A: Curve will have critical point if it have vertical tangent or horizontal tangent . Slope of…

Q: 4. Let S1 : x + y – 2z +1 = 0 and S2 : x² + y – z = 0 be two surfaces. Find symmetric equations of…

A:

Q: 4. Find the equation of the tangent plane to the level surface x4 + yz – yz² + 5x = 0 at 3

A:

Q: Riemann sits on the line normal to the curve y=x2 -3x+2 at x = 1

A: Given           y=x²-3x+2 and x=1  Slope of the curve is given by =dy/dx

Q: Find the family of curves orthogonal to the family 4y2 + 3x2 = k when x > 0 and y > 0. (A) 3y2 – 4x2…

A:

Q: Find an equation of the parabola y = ax² + bx + c that passes through (0, 1) and is tangent to the…

A:

Q: FInd c and d so that the curve y = x3+ cx2+d will have a relative extrema at (2,5). Find other…

A: Maxima or minima: Let f(x) is any function. 1) Evaluate f'(x) = 0 for critical point. 2) Evaluate…

Q: 3. Find the equation of the plane tangent to the graph of f (x, y) = 3x + 4y – xy at the point (1,…

A:

Q: 7 Find the stationary point on the curve e + ye = 2e'. %3D

A: In the given question, the concept of the stationary point is applied. Stationary Point The critical…

Q: Find the equations of the tangent line in the given plane. Tangent to the parabola z = x² + 3y² , x…

A: Given :                    z = x2 + 3y2      at the point (1,2,13)

Q: Find an equation of the tangent plane to the surface at the given point. xy2 + 3x – z2 = 56, (5, -3,…

A: Given:   xy2 + 3x - z2 = 56  Point ( 5 , -3, 2 )