Find an equation of the tangent plane to: 3x +y = z at P(-1,1,-2) %3D

Q: Find the plane tangent to the function, z=x(sqrt(y)) at (3, 49).

A: Given: The function is z=xy and the point is (3, 49).

Q: The parametric form of the tangent line to the image of f(t) = (2t², ?,t +2) at t = 1 is L(t) =

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Q: Find the equation of the tangent plane to the graph of G(u, w) = sin (uw) at the point (r, ).

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Q: t) Find the equation of the tangent plane z = e° + x + x° + 7 at the point (5, 0, 3138). z =|

A: The answer is found in step-2.

Q: Find the tangent to r(t) = (t +1, t², e') when t= 3.

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Q: Find the equation of the tangent plane to z=e^y+x+x^5+10   at the point (3,0,257)

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Q: Find an equation of the tangent to the curve given by = evi y = t – In(?) at the point corresponding…

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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 the equation of the tangent plane to z = ey + x + x2 + 11 at the point (5, 0, 42).

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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: Use the formula for the slope of the tangent line to find Y for the curve c(t) = (t¯1 – 4t, 3t³) at…

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Q: Find an equation of the tangent plane at the given point. f (x, y) = x^2y + xy^3,  (2, 1)

A: To Find an equation of the tangent plane at the given point. f (x, y) = x^2y + xy^3,  (2, 1)

Q: Find an equation for the tangent plane to the function f (x, y) = Jy – x at (1,2,1). %3D

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Q: Find the rightward-pointing (positive x-direction) unit tangent to the curve P = {(x, y) E R² |y =…

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Q: Show that the tangent at P(x,,y,) on the curve -1 Vx+Jy=Ja is yy, ,=a

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Q: Find the value of c such that the line y = (1/6)x + (3/2) is tangent to the curve y = c(sqrt(x)).

A: Solution: Y1=16x+32Y2=cx

Q: The parametric form of the tangent line to the image of f(t) = (4t2, ,t+ 4) at t = 1is L(t) =

A: First we will find the tangent vector by differentiating f

Q: Find an equation of the tangent plane to the graph of F(r, s) at t F(r. s). - (3r4 1 + 1), (-1, 1.…

A: Introduction: Let z=f(x,y) denote the equation of a surface S in R3, and P=(a,b,c) denotes a point…

Q: Find the equation of the tangent plane to z=e^y+x+x^4+6 at the point (4,0,267).

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Q: nd the tangent plane to the equation z = a? – 4y? – 2y at the point ( – 3, 3, – 33)

A: In this question, concept of tangent  is used. Tangent A tangent is the line that runs parallel to…

Q: Find the tangent to y = cos x at x = 5- O A. y=x+7 O B. y= -x+7 O C. y= -x-7 O D. y= 1

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Q: Find the length of the are of the curve п x=e' sint , y=e' cost from t-0 to t=:

A: Given: x=etsint, y=et cost from t=0 to t=π2

Q: 3. Find the slope of the tangent line to r?ey + y²e² = 2e at (1,1). %3D

A: Let's find slope of given tangent line.

Q: Find an equation of the plane tangent to the following surface at the given point. V3 A,1, sin (xyz)…

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Q: find an equation of the tangent plane at the given point. G(u,w) = sin(uw), ( π/6 , 1)

A: Given that: G(u,w)=sin(uw) Now, Find the partial derivatives of Gu(u,w)  and  Gw(u,w) at point π6,1.…

Q: The equation of the tangent line to f(r) = at z = 1 is y = ar +b and the tangent point is (1, c).

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Q: Find the angle between the tangents to the curve R(t) = ti + 2tj – t°k at the points t = +1

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Q: Find all points on the curve e = {{r,y) : x² – ry + y? = 7} where the tangent line to C is…

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Q: Find the equation of the tangent plane to z = ey + x + x² + 7 at the point (5, 0, 38). = Z |

A: To find the equation of tangent plane to z=ey+x+x2+7  at the point 5,0,38In general the equation of…

Q: Find the points on the curve z t? – 10t – 8, y = t² + 4t + 6 that have: A. a horizontal tangent line…

A: Disclaimer: "Since you have asked multiple questions, we will solve the first question for you.  If…

Q: x² = y + 3y.

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Q: Let f(x)= sec(x), find the linear approximation at x= pi/4 and use it to estimate sec(pi/5)

A: Given function: fx=secx At x=π4 fπ4=secπ4=2

Q: For the implicit curve y + xy + x2 = 3, find a point on the curve where the tangent line is…

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Q: Find the equation of the tangent plane to z = e9 +x + x³ + 6 at the point (3, 0, 253).

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Q: Given h(x) = ,(2t? – 4t) dt, write the equation of the tangent line at x = 1. %3D

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Q: The parametric form of the tangent line to the image of f(f) = (4i², 2,t – 3) at t = 2 is L(t) =

A: To find the parametric form of the tangent line to the image of f(t)

Q: Find the equation of the tangent plane to the graph of f(x, y) = 8x² – 2xy? at the point (5, 4). A)…

A: We first find the partial derivatives  So the direction vector of the normal is = (48,-80)

Q: At what point or points is the tangent to the curve C: x = t³,y = 5t², z = 10t perpendicular to the…

A: Given curve is C: x=t3, y=5t2, z=10t

Q: Find all points (x,y) on the curve C:x(t) = t² + 6t + 12, y(t) = 5t – 8 where the tangent line to…

A: We need to find the point (x,y) on the curve C,whose tangent line to the curve is vertical

Q: Find the equation of the tangent plane to f(x,y)=√2xy+ 1 at the point            (2, 2),and use it…

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Q: Find an equation for the tangent plane to the graph of f(x, y) V3+ r2 – 3y2 at the point P(2, 1,…

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Q: Find the equation of the tangent line to a? + y? = 9 at the point (2, v5) O y = 5+ 2 (x - 5) V3 Oy =…

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Q: Find the tangent plane to the curve T = [t, t², t³] which pass through point M (2, –, –6) .

A: If the parametric equation of a curve is given by , then the tangent direction is given by . The…

Q: The tangent line to the graph of y = In(2x) is perpendicular to a + 4y = 1 at the point where Select…

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Q: Find the tangent plane to the equation z x? – 2y + 2y at the point (- 1, 5, – 39). z =

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Q: The parametric form of the tangent line to the image of f(t) = (2t², 3, t - 1) at t = 4 is t L(t) =

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Q: The tangent line to the graph of y = nz is perpendicular to the line z = 7 at the point where Select…

A: Line x = 7 is perpendicular to x axis. A line perpendicular to this will be parallel to x axis.…

Q: Write the equation of the tangent line in Cartesian coordinates for the given parameter t. x = eVE y…

A: at t=1 x=e1=e1=ey=1-ln(12)=1-ln(1)=1-0=1 tangent point (x1,y1)=(e,1)equation of tangent line…

Q: For (z +y)? = z² -f find the points where the tangents are horizontal.

A: