Find the points on the curve y = 14x closest to the point (0, 1). and

Q: Find an equation of the tangent line to the curve 2(z² + y°)² = 25(æ² – y³) (a lemniscate) at the…

A:

Q: 2. Find the tangent lines to the curve y = x4 – 14x2 + 17x + 40 perpendicular to the line x = 7y +…

A: Given, y=x4-14x2+17x+40 Now differentiate with respect to x we get, dydx=4x3-28x+17 The tangent is…

Q: Find the points on the curve 9y = x where normal to the curve makes equal intercepts with the axes.

A: Since, the equation of curve is given by 9y2=x3-(i)⇒y2=x39⇒y=±x33Differentitaing equation-(i) both…

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: Please help me find the length of the curve

A: We\'ll use arc length formula with a=pi/2, b=2pi/3.

Q: Find the exact length of the curve. y = 1 - e-x ,    0≤   x ≤ 2

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Q: Find the equation of the tangent line to the curve y2=6x-3 perpendicular to the line x+3y=7

A:

Q: Find the length of the curve parameterized by x = 2 + 3t² and y = 3 + 2t³ from t=0 tot = 3.

A: A detailed solution is given below

Q: tind the point on the curve y=Jx that is closest to the point (3,0).

A:

Q: Find the exact length of the curve. y = Vx - x2 + sin

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Q: Find the point on the curve y =√ x that is closest to thepoint (3 ,0) .

A: Let (x,y) be the point on the given curve which is closest to the point(3,0) where The distance…

Q: The equation for the tangent line to the curve y=x3 which passes through the point (0,2) is y=mx+b…

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 points on the curve y = 2r3 – 3x2 – 12x + 20 - where the tangent is parallel to the x-axis.

A: A straight line parallel to x-axis have slope 0.

Q: Find the equation of the line that is tangent to the curve r = x In y, x > 0, at the point (1,е).

A: Equation if the line (y - y1) = m(x -x1) D(uv) = uDv + vDu , where D is the differentiation of…

Q: (b) Find the points on the curve y = 2x3 – 3x2 – 12x + 20 where the tangent is parallel to the…

A:

Q: Find an equation of the line tangent to the graph of y sin x – 3y = 4 at the point %3D (, 4) .

A: y2sinx - 3y = 4 at (π/2 , 4) we have to find slope of function 2ysinx(dy/dx) + y2cosx -3dy/dx = 4…

Q: Find the equation of the tangent line to the curve at the given point. y = 9x – 8/x, (1, 1) %3D

A: Given,           Equation of the curve is y = 9x -8x  and point = (1,1)

Q: Find the exact length of the curve.y = 9 + 1/7 cosh(7x),  0 ≤ x ≤ 6

A: Given that: To find: Exact length of the curve

Q: Find the exact length of the curve. y = 9 +  1 7  cosh(7x),  0 ≤ x ≤ 6

A:

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

A:

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

A:

Q: 2. Find the point on the curve y = VI thats is closest to the point (3,0)

A:

Q: Determine the coefficients a, b, c and d so that the curve y = ax* + bx³ + cx² + dx + e will pass…

A: Since we have to find value of a,b,c and d

Q: Find the point on the curve y = Vx +1 that is closest to the point (5,0)

A: We will use second derivative test to find the smallest distance among point (5,0) and curve

Q: Find the exact length of the curve. y2 = 16(x + 4)3, osxs 2, y > 0

A: Given data:   The given expression is y2=16(x+4)3. The given limits of x is [a,b]=[0,2].   The given…

Q: Find c so that the line y = 4x + 3 is tangent to the curve y= x^2 + c?

A:

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: Find the exact length of the curve. y = In(sec(x)), 0 <x< a/6

A:

Q: Find an equation of the tangent plane to the graph y = x² + 2xz at (1,3, 1). (Possible Answer: 4r –…

A: We have to find an equation of the tangent plane to the graph y=x2+2xz at 1,3,1.

Q: Find the closest point to the point (2,0) on the y = x curve.

A: To find the closest point to the point (2,0) on curve y=x

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

A: we will see in next step

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 a point on the curve y = x2 that is closest to the point (18; 0)

A:

Q: Find the length of the curve defined by Y=5x^3/2+9y from x=1 to x=8.

A: Given that

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: Find the equation of the line tangent to the curve y=x+cosx at the point (0,1)

A: Given, curve and point

Q: The slope of the tangent to the curve y²x + y²a² = 6 at (2, 1) is A B) -1 в 14

A: We can find the slope of the tangent to the curve at the indicated point as below.

Q: Find the exact length of the curve. 1 + 8. X = 1 s y < 3 4y2'

A:

Q: Find the exact length of the curve. x = Vy (y - 3), 9 < ys 25

A: It is given that x=13yy-3, we need to find the exact length of curve.

Q: Find the equation of the tangent line to the curve y = + 6x at its point of intersection with the…

A: The tangent of any given function is the line that touches the curve of the function at only one…

Q: Consider the curve given by y2 + (1+x³)³ = xy + 10. Find the equation of the tangent line to the…

A: Considering the curve- y2+1+x33=xy+10 Firstly, find the slope of the curve. dy/dx is the slope of…

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

A:

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

A:

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

A:

Q: Find the exact length of the curve. y = 9 + ¹ cosh (8x), 0≤x≤7

A: The curve y=9+18cosh8x, 0≤x≤7

Q: Find the points on the curve y = 2x3 + 3x? – 12x + 9 where the tangent line is horizontal. (x, y) =…

A: we have to find the points on the curve where the tangent line is horizontal. y=2x3+3x2-12x+9