9. Find fpF dr, where P is the line segment from (0,0) to (1,0) and F(x, y) = (137).

Q: the line (x/a)+(y/b)=1 moves in such a way that (1/a\power{2})+(1/b\power{2})=(1/c\power{2}) ,where…

A: Variable line is                xa+yb=1                 ......(1)Any line perpendicular to (i) and…

Q: Find y as a function of a if y(0) = 7, y/(0) = -12, y'(0) = 108. y(x) = y" + 36y' = 0,

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Q: Find the linear approximation L(x of the function f(x) =V1– at a = 0. L(x)=mx+b where m is - and b…

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Q: Find y as a function of t if y(4) = 6, y (4) = 4. y = 121y" - 132y +36y = 0,

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Q: Find the line tangent to the curve x 3 + y 3 4 at the point (-3/3, –1). V3 y = 3 x – 4 V3 4 - 3 -V3…

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Q: Equation: Answer:

A: We want to find value of x. For this we use Pythagoras theorem, which states that Hypotenuse2 =…

Q: Evaluate where F(x, y) = x² i+(y² – x) j and C is the line segment from (2, 4) to (0, 4) followed by…

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Q: 16. Find the values of r so that the function y= e™ satisfies the equation y" – 4y' – 21y = 0. A)…

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Q: The equation of the tangent line to the curve x² + y? = 9, at (7,-18) is 7 y = 18 7 (х — 7) — 18 18…

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Q: +3. . Find the linearization of _9). Can you tell anything about the error? at (3,2). Evaluate at…

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Q: 8. Let a2 + xy³ + 2x = 11. Find y"(x) at the point (1, 2). %3D

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Q: Find the function r that satifies the following condition. r'(t)=(3t2,4t3,2t); r(1)=(-2,-5,-9)…

A: Given,          r't= 3t2 , 4t3 , 2t  , r1=-2,-5,-9

Q: let r (t) = The y component of r' (5)

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Q: Consider Flx,y) = (3x2 +6y) i t (6x +4y%)j. (as Show that Fis lonservative a function Such Line…

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Q: Find the orthogonal trajectories of the family of curves y = kx'. = C (C) 3 y³ +x? = C (D) 3 y³ + 3…

A: Given y5=kx5 To find the orthogonal trajectory

Q: Let 7(t) = (- 5t + 2, t² – 4t³, 3tª). Find the line (L) tangent to 7(t) at the point (7, 5, 3) L:(x,…

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Q: If (X, d_{1}) and (Y, d_{2}) are metric spaces, we define d: (X × Y ) × (X × Y ) \rightarrow R by…

A: Let X be a nonempty set with a mapping d:X×X→R is said to be a metric space if mapping d…

Q: Find y as a function of a if y(0) = 2, y(0) = 3, "(0) = 7. y(x) = y"9y" + 18y = 0,

A: y'''-9y''+18y'=0y(0)=2, y'(0)=3, y''(0)=7To Find: y(x)

Q: Use Linear Approximation to estimate the change, Az, in z = 8x2 + y? as (x, y) changes from (2, 3)…

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Q: uppose that x + y = 2. What is y" at the point (1, 1)?

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Q: 16xydx- 24ydy = -8x²dy %3D

A: The given differential equation can be written as:16xy−24yy' =−8x2y' An ODE Mx, y+Nx, yy'=0 is in…

Q: Compute F. dr where F (x,y) (6x + y) i+ (4y + x)j and C is a piecewise curve from the point (1,1) to…

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Q: Find ∫F • dR from (1, 0, 0) to (1, 0, 4), if F = xi - yj + zk along the line segment joining (1, 0,…

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Q: Find y as a function of a if y(0) = 12, y(0) = 21, y"(0) = 18. y(x) = y" 16y" +63y = 144e²,

A: Given: y'''-16y''+63y'=144ex y0=12 y'0=21 y''0=18 To find: Solution to the given differential…

Q: Find the slope for f(x,y) = xeyat P (2,0) in the direction of the line from M(2,0) to N(-1,2)

A: We have to find slope