Find the slope of the curve Y = Vx at the point P (4, 2).

Q: Find an equation for the line in the xy-plane that is tangent and normal to the curve x³y² + y² = x…

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Q: Find equations of the tangent and normal line to the curve x? – xy – 3y2 = -4 at (1,2).

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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 an equation of the tangent line to the curve y=2x2+3 that is parallel to the line 8x-y+3=0. а.…

A: Topic:- application of derivatives

Q: Find the equation of the tangent line on the curve x2 + y2 + 2y=0 at (0, – 2). A y= - 2 B) y= - x…

A: In this question we have to find the equation of the tangent line on the given curve.

Q: Find an equation of the line tangent to the curve y = e at (0,1). 2x

A: We need to find the equation of tangent to the curve: y=e2x  at (0, 1) This can be done as follows:

Q: Find an equation of the tangent line to the curve at the given point. y = Vx, (64, 8)

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Q: Find the equations of the tangent lines x = t3 − 6t, y = t2 at the point where the curve crosses…

A: To find the equations of the tangent linesx=t3-6t,y=t2 at the point where the curve crosses itself.…

Q: The point on the curve y=vx+2 which is closest to the point (5,2) is

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Q: Find an equation of the tangent line to the curve at the given point. y = Vx, (1, 1)

A: Given: To find an equation of the tangent line to the curvey=x at the given point (1,1)

Q: (b) Find the equation of the line normal to the tangent at the point (1,4) on the curve x'y+ xy =…

A:

Q: What point on the curve y = Vx is closest to the point (5, 0)?

A: Use distance formula between two point and then differentiate

Q: Find the equation of the curve, if at any point on the curve y "= 1- vĩ and it has a tange line at…

A:

Q: Find the equation of the tangent line drawn to the curve y4−4x4−6xy=0 at the point M(1,2).

A:

Q: Find the equation of the tangent line at the given point on the curve. 2y- Vx 28, (16,4) y=D

A: 2y2-x=28,    16, 4. Slope of the tangent line is the derivative of the given function at the given…

Q: Find the equation of the line tangent to the curve 3t2 + 8,y = 8t + 3 at t = 2

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Q: Find an equation for the line tangent to given curve y = -10z2-3 4r+1 3 at x = 0-

A:

Q: Find the equation of the tangent line to the curve x=t2−2t, y=t2+2t at the point t=2.

A: Given equation of curve is Now,

Q: (B): Find an equation for the tangent and normal Line to the curve (y 2x +4x-3) at (x1)

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Q: Find the slope of the tangent line to the curve 3x? + xy – 4y³ = 6 at the point (1, – 1).

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Q: Find an equation of the tangent line to the curve at the given point. y = Vx, (25, 5)

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Q: the equation of the tange

A: Given that: The equation of the curve x2 + 4y2 = 8. The equation of the line x + 2y = 8.

Q: Find the equations of the tangent lines x = t2 − t, y = t3 − 3t − 1 at the point where the curve…

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Q: (b) Find the equation of the line normal to the tangent at the point x’y+xy² = 6.

A:

Q: The slope of the curve y = (5x² + 8x + e)eje at x = 0 is

A:

Q: Find the slope of the tangent line to the curve Ar 3ay + 2y°= 3

A: Given,         The curve is 4x2-3xy+2y3=3 at the point 1,1.

Q: find the slope of the curve x = e^-tcost2t, y=e^-2tsin2t at the point t= 0

A: find out the slope of the curve at t=0

Q: Find an equation of the tangent plane to the graph z = Væ + y³ nt (8, 2, 4).

A: We know that equation of tangent plane to the graph z=f(x,y) at point (a,b,c) is…

Q: Find the slope of the tangent line to the curve (r² + y² – 1)3 – r²y³ = 0 at the point (–1,1).

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Q: Find an equation of the curve y = f(x) if y^n = 6x and the tangent line to the curve at (1, 2) is…

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Q: Find the equation of the tangent line to the curve at the given point. y = v2x + I, (4, 3)

A: →Slope, m = dydx→dax+bdx =12ax+b→Equation of straight line passing through (xo,yo) with slope m is…

Q: Find the slope of * y+ Vx+ y =x at (3,1)

A: A detailed solution is given below

Q: Find the slope of the tangent line to the curve 3z? – 2xy – 3y3 = 63 at the point (3, – 2).

A: topic - slope of tangent line to curve

Q: At what point on the curve x = 3t2 + 4, y = t³ – 6 does the tangent line have slope ? (x, y) = ( 3,…

A:

Q: Find the equation of the tangent plane to the graph of f(x, y) =−3x2 − y3 at the point (x, y) = (2,…

A: The given function is

Q: Find a point on the graph where x = t² - 1, y = 2t has a vertical tangent.

A: For vertical tangents dx/dy=0

Q: Find the point(s) on the curve t3 3t, y 2t2 +t 2 x = - where the slope of the tangent line is equal…

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Q: Find the orthogonal trajectory of the curve x^2 + y^2 = 2 ln x

A: See the details solution in below

Q: Find the point on the curve y=/2 for which the tangent ine to the curve is perpendicular to the line…

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Q: Find the slope of the tangent line to the curve 2a? – 4xy – 4y³ = 4 at the point ( – 2, – 1).

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Q: Find an equation of the tangent line to the curve at the given point. y = v x, (81, 9) y = |0

A: y = xdifferentiate with respect to x,dydx= 12xdydx(81,9)= 1281=118

Q: Find the equation of the tangent line to the curve y = e' when it is paralel to 2r-y =7.

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Q: find the equation of the line tangent to the curve y2+ exy=4 at point (0,2)

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Q: Find an equation of the tangent line and normal line to the curve at the given point. y = x* – 2e*,…

A: Given curve is y=x4-2ex. To find the equation of the tangent line and normal line to the curve at…

Q: 2. Find the slope of the tangent line to the curves: (a) xy + y³ = 12 at the point (2, 2), (b) 3x4/3…

A: This question can be solved using the concept of tangent and normal using application of…

Q: Find the equation of the line normal to the curve 2x^2-3xy+y-18=0 at (3,0).

A:

Q: 2. Find the equation of the line that is tangent to the curve y 3 + 3y = x 2 at the point (2, 1).

A: Find the equation of the line that is tangent to the curve y3 + 3y = x2 at the point (2,1).

Q: Find an equation of the line tangent to the curve y = v4x – 3 – 1 and perpendicular to the line x +…

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Q: At what point on the curve x = 3t2 + 1, y = t3 – 5 does the tangent line have slope ? 2

A: