Q: Find an equation of the tangent to the curve at the given point by both eliminating the parameter…
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Q: Find the derivative of the parametrically defined curve (t) = 2 cos(4t), y(t) = sin(4t). dz 4cos4t…
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Q: Which of the following points do not lie on any tangent line of the parabola y=x2+2
A: given parabola is y=x2+2 any point on the…
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Q: Find an equation for the tangent to the curve y = 18 at the point (1,6). 2. X +2 O A. y= - 4x + 10 O…
A: The equation of tangent y = -4x +10 Hence option (A) is correct
Q: Find the second derivative of the parametric equation ; x = t3 + 1, y = 4t2 −4t.
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Q: Find the equation of the tangent line to the curve ³+y³ = 9 at the given point (1, 2). a. 4x-2y=10 O…
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Q: 2- Find the equation of the tangent line to the curve 7xSin(3y) + 5y = 7 at y = C
A: Given problem:- Find the equation of the tangent line to the curve 7xSin(3y) + 5y = 7 at y = 0
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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 derivative 4cos4t sin4t 2cot4t -1/2 cot4t Other: of the parametrically defined curve : x(t)…
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Q: Find an equation of the tangent to the curve at the given point by both eliminating the parameter…
A: Explanation of the solution is given below..
Q: Consider the smooth parametric curve defined by the equations = t (t² − 3) = 3 (t² − 3)' X Y where…
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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: 2. Calculate the derivative dy for the parametric equation x = t² + ³ + ln(4t+1), y=e5t² giving your…
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Q: Find the derivative of the parametrically defined curve (t) = 2 cos(4t), y(t) = sin(4t).
A: We have to find dy/dx.
Q: find the values of the derivatives
A: Given: w=z+z first we differentiate given expression with respect to z then substitute z=4
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Q: Find the derivative of the following functions/parametric equations. 6. 4 cos x sin y = 1
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Q: (a) Find the slope of the tangent line to the parametric curve x = t² + 1, y = t/2at t = −1and t = 1…
A: Given, x=t2+1, y=t2, and t=-1, t=1
Q: Find the equation of the tangent line to the parametric curve at (9,2). x = t3 + 1 y = t2 - t
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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 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 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: f(x,y) = 4x² + y² + 2 at the point wherex = 1 and y = 1.
A: The equation of the tangent at point (1,1) is: z=f(1,1)+fx(1,1)(x-1)+fy(1,1)(y-1)
Q: Find the derivative of the following functions/parametric equations: 8. x = 3t – 5|y = t² – 6t + 4
A: Given:- x = 3t-5 y = t2 -6t+4 To find:- Derivative of given parametric equations
Q: Find the derivatives of the following functions: Inx i) y = sin3x? ii) y = e2*cosx iii) y = 3r+5
A: i)y= sin 3x2y' =ddx sin 3x2y' =cos 3x2 ddx(3x2)y'=cos 3x2 (3)(2x2-1)y'=(6x) cos 3x2
Q: Find an equation of the tangent line to the curve y? = x3 + 3x? at thu point (1, 2). 2у + 3x 3 3 3x…
A: We have to find the equation of tangent line.
Q: Which of the following is the equation of the tangent line to the curve y = 6x + 10x* + 2 at its…
A: An inflection point is a point on the graph of a function at which the concavity changes. Points of…
Q: Find the equation of the tangent line to the parametric curve. x = t1/2 y = t2/3 at t = 1. Also…
A: The curve is defined by the parametric equations as x(t) = t1/2 and y(t) = t 2/3 Apply the chain…
Q: Find a parametric equation for the tangent line to the curve defined by r(t) = when t = 1.
A: Given is the equation of a 3-dimensional parametric equation, to find the equation of the tangent we…
Q: Find the second derivative of the parametric equation = 9t2 + 4 , y=3(t − 2)2
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Q: Find an equation of the tangent line to the curve defined parametrically by x =? -t and y =t- 32 + 9…
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Q: Q7// Find tangent and normal equations of the curve x³ + y3 – 9xy = 0 at points (4,2) and (2,4).
A: The slope of a curve at the point (x1, y1 ) is given by;…
Q: The parametric equations of a curve are given by x = In (Vi +1) and y = cosh (2t). dy Find the…
A: Use chain rule of differentiation to solve this problem.
Q: The equation of the tangent line to the curve x2 + y? = 25, at (8,-12) is. %3D 8. (x +8) + 12 12 y =…
A: differentiate equation with respect to x. 2x+2y(dy/dx)=0 (dy/dx)=-x/y so, m=(dy/dx)|(8,-12)…
Q: Find the derivative of the following parametric equations. (a) x = t2 + 5t + 4, y = 4t (b) x = 0 –…
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Q: Find the 3rd derivative of the function given by the parametric equations x=1+t2, y=t−t3 at t=1.
A: Differentiate x and y with respect to t.
Q: - Find an equation of the tangent line to the curve sin(r+y) = 2y – 21 at the given point (-7, –x).
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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 the curve defined by the equations a = t +, y =t – when t =…
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Q: Find the derivative of the following functions/parametric equations: 5. y = 2cotx
A: We have the basic derivative ddx2x=2xln(2)
Q: 2 Calculate the (d^n*y)/(dx^n) derivative of the curve with the parametric equation x=lnt, y=t^alpha
A: The given problem is to find the nth derivative of y with respect to x of the given parametric…
Q: Find an equation of the tangent line to the curve at the given point by both eliminating the…
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Q: Calculate the derivative dy for the parametric equation x=t7+t³+ln(5t + 1), y = e4t²_ +t6 giving…
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Q: Find the derivative of the following functions/parametric equations. 4. e2x cos y + y2 = 1
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Q: VI. x = v1 - t , y = t³ – 3t
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Q: d²y if x = 21? - 3 & y = 3 – 1*. dx Using parametric differentiation, find
A: dy/dx=(dy/dt)/(dx/dt)
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