Let S(x, y) = x2 + y2 1. Find the equation circle orthogonal to S and passing through the intersecting points of S = 0 -2x- 16y + 10 0 be a circle and L(x,y) =x-5y+10 0 be a line. %3D and L = 0. 2. Find the equations of tangent lines from S = 0 from the point A(0,0).

Q: dy Find dæ Given that y = 3u² – 7u + 5 and u = 6a² + 4x – 1. 1. 2. Find an equation of the tangent…

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Q: Find dy/dx and d^2y/dx^2 X=t-e^t, y= t+e^-t For which values of t. Is the curve concave upward?

A: Given that, x=t-e^t, y= t+e^-t

Q: 21 Given the curve x + y? + py –q =0 where p and q are constants. dy a. Find dx b. If the gradient…

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Q: Consider the curve defined by x2y + 3x + y2 = 38. a. Find dy/dx dy dx .   b. Find an equation of…

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Q: Find an equation of the tangent line at x= a. x- y%3D a = 2 4 10 A. y=x+1 *B y=x-1 y3x-1 Xe y=x+2…

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Q: A heat-seeking particle is located at the point P(6,4) on a metal plate with temperature at (x, y)…

A: Given, a heat seeking particle is located at the point P(6, 4). The temperature function is given…

Q: :a stream function is given by: Y=2x²y + (x+t)y2 Find the velocity equation for flu me = 1s?

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Q: Express the curve by an equation in x and y given x(t) = e' and y(t) = 7 – e2'. a) O-x2 + y = 7, x 2…

A: simplify the equation and choose correct equation.

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

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Q: (aj.G) x - 3x 4 3, find G'(a) and use it to find equations of the tangent fines to the curve y=x…

A: Given that       G(x) = x2 -3x+3  Here we have to find G'(a) and by using it find the equations of…

Q: Find the points on the curve x = t – 16t - 3, y = t + 6t + 8 that have: %3D A. a horizontal tangent…

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Q: The curves C,:x=t, y=t, z=t, t20 and C,: x= sint, y 1+cost, z=1, 120 have intersection at the point…

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Q: 7. a. Find the points on the curve x = 3(t2 – 3), y = t³ – 3t where the tangent is horizontal or…

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Q: %3D Find the equation of the tangent line at (1, 1) of 6x²y- ncos(y) = 7m y= -2nx +3T B y=2nx+3n C.…

A: Solving the problem by doing the derivative and then calculate the equation of tangent line.

Q: For the curve y = f(x) = x², 0 ≤ x ≤ 2, its length is 2 L = 1+ dy dx dx =

A: Given curve y=f(x)=x2,0≤x≤2 The objective is to find the length of the curve.

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: Find the point at which the curve Sx=f +19 Ly=d-4t has a vertical tangent. (x, y) = (

A: Given: The curve is given as x = t5 + 19, y = t4 - 4t   To find: The point (x,y) at which the given…

Q: The curves y = In x and y = 3x² have parallel tangent lines at x = A) ± √/ B) C) √6 E) 2

A: Two lines have parallel tangent if slop at the point is same.

Q: y = e*, 0<z<1.

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Q: ) Find the gavea d the rgion enclased by the line x-In3 and the curves y= ex and y=ex

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Q: 20. The curve 2x2y+ y 8x +1 passes through (4, 1). Using the tangent line to the curve at the point…

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Q: Find the linear approximation to the equation f(r, y) = 4 ln(z – y) at the point (2,15,0), and use…

A: Given: fx,y=4lnx4-y We have to find the linear approximation in two variables.

Q: Below is a plot of a cardioid, which consists of points satisfying x² + y² = (2x² + 2y² - x)² 0.6…

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Q: dy Find for the curve x-2.x'y-20y 2 at point (-2,1). de

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Q: If the equation of the tangent plane to x2+y2-11z2=0 at (1,1, /2/11) is x+ay+Bz+y=0, then a+B+y=D

A: Given query is to find the equation of the tangent to the plane.

Q: Find the conditions such that the equation M (x, y) dx + N (x,y) dy = 0 mogeneous and exact.

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Q: H.W 2-Write the tangent line equation. P. (J2. V2) P.(7,1) (1) x²+y² = 4 %3D (2) x²-y =1 (3) xy =-4…

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Q: Find the value of c such that line y=3/2x+6 is tangent to the curve y=cx1/2.

A: Given,  line y=3/2x+6 is tangent to the curve y=cx1/2.

Q: A heat-seeking particle has the property that at any point (x, y) in the plane, it moves in the…

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Q: The length of the curve y = Ey3/2 between x = 0 and X 1 is %3D

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Q: Find f(x) if y = f(x) satisfies dy = 91ya"2 dx and the y-intercept of the curve y = f(x) is 5.

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Q: Integrate f(x,y)=x²-7y over the curve C: x² + y² = 64 in the first quadrant from (0,8) to (√32.√32)…

A: Draw the given equation of the curve x2+y2=64 and the given points. The given curve is between…

Q: If the equation of the tangent plane to x2+y2-147z²=0 at (1,1,/2 / 147) is x+ay+Bz+y=0, then a+ß+y=

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Q: Find f(x) if y = f(x) satisfies dy 50yz da %3D and the y-intercept of the curve y = f(x) is 2.

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Q: Find the values of dz/ôx and az/ðy at the points 31. z - xy + yz + y -2 = 0, (1, 1, 1)

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Q: [&+2y)dx +(x² - 3y°)dy (3+2 4. Evaluate where C is any smooth curve from the point A (1, 0) to the…

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Q: Find the equations of the tangent and normal line 4x2 + y? + 8x + 2y = 20 at x = -3 %3D

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Q: Consider the curve given by y2+xy=x3-(2y/3)+(3x2/4) a) Find all the points (x,y) on this curve…

A: Given is the equation  y2+xy=x3-2y3+3x24..............................(1) The objective is to find…

Q: Find [(dy)/(dx)] if the curve is defined by 7 x² e7 Y + 6 y2 e2 x = 16. %3D [(dy)/(dx)]

A: Given:     7x2 e7y + 6y2e2x = 16

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

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Q: Find the equation of tangent line to the parabola y² = 6x – 3 which is perpendicular to the line x +…

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Q: -38x^8+10x^76y+y^9=-27, find the dy/dx. Now find the tangent line to the curve (1,1). Write in…

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Q: (2) Find an equation of the straight line tangent to the given curves at the indicated points: (a) y…

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Q: Find the equations of the tangent and normal lines x^2 + 2y^2 = 9 TL I to the line x + 3y = 7

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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: dy lat dy %3D dx dt 5) Find the equation of the line tangent to the curve using the fact that: For…

A: Given equation is Differentiating with respect to , we get   Now, Now, t=e corresponds to given…

Q: Find the equation of the line through the origin auel normal to the line x=y-S,2:2y-3?

A: Let ,     L1 : x-01=y-51    L2 : y-321=z-02L be the required line which passes through 0,0,0 &amp;…

Q: xe" dx+x²ydy Compute e'dr+r'ydy along the curve C: * = 31, y =t² ,0<ISI

A: Topic: application of integration

Q: Integrate h (x, y. 2) = yzi+xj+xzk over the indicated path: (a) the line segment from (0, 0. 0) to…

A: definite integrate calculus