Find an equation of the tangent plane at the given point: F(r, s) = – (2r4. 1 2), (-2,1) s0.5 = Z

Q: Find the points on the curve a = t – 16t + 1, y = t² + 12t – 8 that have: %3D A. a horizontal…

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

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Q: Find the equation of the tangent line to the curve when x has the given value. f(x) = x – x; x = 4 O…

A: Given curve is Differentiating with respect to x , we get Now, we will find f(4) and f'(4)

Q: Given f(z) = x+ VE Calculate the tangent line at the point (16, 20) y : (2- 16) + 20

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Q: Find the equation of the tangent plane to 4 = Z = eª + x + x* + 4 at the point (1, 0, 7).

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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 points on the curve æ = t² – 6t – 8, y = t² + 14t – 6 that have: A. a horizontal tangent…

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Q: Find the equation of the tangent plane to the graph of exy² + zy¹ = 61+1 at the point (0, -2,6).…

A: The gradient of a surface includes the partial derivatives of the function. It is always directed in…

Q: Find the interval on which the curve dt 3 +t + 212 y = is concave upward.

A: Given: y=∫1x13+t+2t2dt

Q: Find the equation of the tangent line to the curve r(t) = [3+2cos(t).-3+2sin(t), 2] at the point…

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Q: Find the slope of the tangent line for the curve r= 2cos 30 at the point where 8 = a) 1 b) - V3 c)-6

A: Given curve r=2cos 3θ Point θ=π6 Differentiate r with respect to θ drdθ=ddθ2 cos 3θdrdθ=-6sinθ We…

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: Find the equation of the tangent line to the curve x = In t ,y =1+t² when t = 1 . %3D

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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: Find the implicit equation of the tangent plane to z = In(x² + 1) + y² at the point (0, 4, 16).

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Q: Find an equation for the tangent line to the parabola y = x² at the point P(1, 1). A y=2 B) y = x…

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Q: find an equation of the tangent plane at the given point. f (x, y) = x2 + y−2, (4, 1)

A: To find equation of tangent plane at (4,1)

Q: Find the equation of the tangent plane to z = e + x + x³ + 9 at the point (2, 0, 20). z =

A: According to question We have to calculate the equation of the tangent plane .

Q: Find an equation for the tangent line to the parabola y = x² at the point P(1, 1). A y=2 B) y = x…

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Q: Find the equation of the tangent plane to z = In(x²y) – x/y at (-;4).

A: Let x0,y0 be any point of surface function z=fx,y. Then the surface has a non vertical plane at…

Q: find an equation of the tangent plane at the given point. f (x, y) = x2y + xy3, (2, 1)

A: Let z = f(x, y) is any function and let x0, y0 be a point on f then equation of tangent plane is,…

Q: Find the points on the curve  x=t^2−18t−4, y=t^2+10t+6   that have: a) a horizontal tangent line,…

A: We have to solve by derivative rule

Q: Find an equation of the tangent plane at the given point: F(r, s) = r²s-0.5 – 2s-4, (-1, 1) z =

A: The formula to find the equation of a tangent plane at a point (a, b) to a given surface f(r,  s) is…

Q: Find the point at which the tangent to the curve y = v V4x2 +1– 2 | has its slop 2

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Q: Find the points on the curve t2 – 14t – 1, y = t² + 6t + 5 that have: х — A. a horizontal tangent…

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Q: Find the equation of the tangent plane to z = ln(x³ + 1) + y³ at the point (0,6,216).

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Q: Find the point(s) (x, y) on the function f (x) = V1+ 2x where the tangent line is parallel to the…

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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: 2y+ In(xy) +z = 6 at the point (4,0.25, 2)

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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: Find the equation of the tangent plane to f(x, y)= x´ – x y – y at point P (1, 1, -1).

A: Consider the equation

Q: Determine the slope of the tangent to the curve 1 Ax) = Vx + ÷+2 at x = 1 %3D A D을 1 B글 C4

A: Given f(x)=x+1x+2 at x=1 Find Slope of the tangent to the curve at x=1 slope,m=f'(x) at x=1

Q: Find the equation of the tangent plane to z = e" + x + x² + 6 at the point (5, 0, 37).

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Q: Find the slope of the tangent line to the curve I defined b y 5x²+8xy-4y"= 1B47 atthe point %3D…

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Q: Find an equation for the tangent line to the curve parametrized by a = t¹ — 1 and y = t5 + t at the…

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Q: Find the slope of the tangent to the curve f(x)=vx at (1,-3). O a. 7.5 O b. 4.5 O C. 8.5 d. 9.5

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Q: Find the slope of the tangent line to the cerve, x-xy°+Iny= 24 at the point C3,2)

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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 points on the curve x = t2 14t + 1, y = t + 12t +1 that have: A. a horizontal tangent line…

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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 of the tangent plane to the graph of f(x, y) = 9x at the point (2, 9 Vy z =

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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: Determine the equation of the tangent line to the curve y=Vx at the point (1,1) (A x-4y+3=0 (в)…

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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: Find an equation of the tangent line at the point indicated. s(t) = In(7 – 3t), t= 1. %3D (t-1)…

A: Following steps help to find equation of line tangent . 1.Find the first derivative of f(x). 2)…

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…