I= e", y =t e", teR,

Q: For which values of t is the curve x = ln t, y = et concave up?

A: given curve x=lnt  , y=et

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

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Q: verify that the given point is on the curve and findthe lines that are (a) tangent and (b) normal to…

A: We plug x=√3 and y=2 in the given equation So the point is on the curve

Q: 5) Sketch the curve X = e', Y = e?t + 1

A: Given, The curve  X = et  and  Y = e2t+1 We have to sketch the curve.

Q: Find the length of the curve described by y = V sec* t – 1 dt, - sI 4 4 (a) 4 (b) (c) (d) 2/2 (e) 1

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

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Q: Consider the curve in the xy-plane repre- sented by = e' and y = The slope of the line tangent to…

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Q: H.W: Find the lines that are tangent and normal to the curve y=tan x at the point (,1).

A: We have to find the derivative of the function first.

Q: Find the distance between the point (-2m, 0, -m) and the tangent line of the curve ū(t)= (me* – }i--…

A: Given: u-(t)=(met2-t)2i-4mt+1j+t-mt2+1k at t=0 First we will find tangent line of the curve…

Q: Sketch the curve by eliminating the parameter, and indicate the direction of increasing t at t = 0.…

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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: 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: H.W: Find the lines that are tangent and normal to the curve y- tan x at the point ,1).

A: Find the equation of line

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: At the given point, find the line that is normal to the curve. 2x y-cos y 3x, (1,x) 1 O A. y= -7**7…

A: The given curve is 2x2y – π cosy = 3π and the point is (1, π). Evaluate the slope of the tangent to…

Q: Find an equation of the tangent to the curve at the point corresponding to the given value of the…

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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: The Normal to the curve 2x2 – y? = 1 at the point (1,1) is: %3D 3 y =-*+ y =x+ y = 2x + 1 %3D P. y =…

A: To find The equation of normal to the curve 2x^2-y^2=1 at the point (1,1)

Q: 21 Find the value of c such that the line y = -x + is tangent to the curve y = c/x.

A: Given line ⇒y = 76x+212    .....(1)curve y = cx   ....(2)Differentiating w.r.t 'x'       (2)y' = c2x…

Q: Find the condition that the line x cos a + y ain a =p may touch the curve yh =1. am bm

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Q: The Tschirnhausen cubic is the curve given by the equation x^2=y^3+3y^2 At which point(s)…

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Q: Find the length of the segment of the curve y = f (x) = e ^ x between the abscissa points x = 0 and…

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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: Find the slope and concavity of the curves at the given points. r = eθ, θ = 0, π

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Q: compute the length of the curve over the given interval.  r(t) = (cost,sin t,t3/2), 0 ≤ t ≤ 2π

A: Derivative of a function is represented as the change in variable with respect to change in another…

Q: 11.What is the slope of the tangent line to the curve y = 3x? – 5 at poin - O A. -7 О в. -5 O C. -6…

A: Differential equation

Q: (b) Find the lines that are (i) tangent and (ii) normal to the curve at the given point: x° cos?…

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Q: Find the point on the curve y = Vx closest to the point (1,0).

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

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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: Find the point on the cycloid c(t) = (t − sin t, 1 − cos t) where the tangent line has slope 1/2.

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Q: Find the length of the curve y = V- from z =1 to r = e. 3

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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: The parametric curve x(t)=t−2t6 and y(t)=t7+2t2 is given. In which case is the tangent line at the…

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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: The slope of the tangent line to the curve r = t2 + 1, y = t+t at t = 1 is (A) 3/2 (B) 2 (C) 4 (D)…

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Q: Find the length of the curve x=e^t -t, y=e^(t/2), -8 less than or equal to t less than or equal to 3

A: The arclength for parametric curves is: L = ∫ab(dxdt)2+(dydt) Given  x=et-t, y =et2,      -8≤t≤3

Q: Find the angle between the curve 2y = e – x/2 and y – axis

A: Given the curve 2y =e^(-x/2) and y-axis We have find angle between curve and y-axis

Q: 3. Find the value of c such that the line y = x + 3 is tangent to the curve y = cvx. C =

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Q: Find the equation of the line that is normal to the curve x cos(xy² – y) = (x + y)² at the point…

A: here option c is true

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: AMoving to the next question prevents changes to this answer. estion 1 * at (4, - 4)? What is the…

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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: A curve in space is given by C = { (r, y, z) = cos(nt) ', In(10 – t²), ² + 4 for t € (0, v10) Give…

A: