An equation of the line tangent to a curve at the point (1, 3) is y = x+2. If at any point (x, y) on the curve, d?y 6x, find an equation of the curve dx? that satisfies the given conditions.

Q: a. Given that x? + y? = (2x² + 2y -x*)* Find an equation of tangent line to the curve at point (0,…

A: NOTE: Hi! Thank you for your question. As per the honor code we are allowed to solve one question at…

Q: 3. The slope of tangent line at any point (x, y) on the curve is 3x²-2x+7. What is the equation of…

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Q: The curve y = ax + bx + c passes through the point (2, 28) and is tangent to the line y= 4x at the…

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Q: The slope of the tangent line at any point (x, y) on a curve is 2yx. If the point (9, 3) is on the…

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Q: Consider the curve defined by x2y + 3x + y2 = 38. a. Find dy/dx dy dx .   b. Find an equation of…

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Q: (a) The curve with equation y 2   = x3 +3 x 2  is called theTschirnhausen cubic. Find an equation of…

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Q: 5 Find the equation of line tangent to the curve y= X+- at point P(1,3) А) 4x +у-7- 0 B None of the…

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Q: Find the equation of the tangent line to the curve (a lemniscate) 2(x^2+y^2)^2=25(x^2−y^2) at the…

A: Given: 2x2+y22=25x2-y2 at point -3,-1

Q: 2) Consider the curve defined by -8x² + 5xy + y³ = -149 dy a) Find dx b) Write an equation for the…

A: solution is given below

Q: The equation of the tangent line to the curve y = 1 at the point (3,-) is Vx +1 A. x+16y +11=0 B. x+…

A: Please refer the attached solution. None of the option is correct here . I have solved it…

Q: The curve y=ax^2+bx+c passes through the point (1,9) and is tangent to the line y=3x at the origin.…

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Q: 1. Find the equations of tangent and normal lines to the curve whose equation y? – 6x² + 4y + 19 = 0…

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Q: The curve C with equation y = f(x) passes through the point (1, -3). Given the following, find f(x)…

A: We know, ∫xndx= x(n+1)/(n+1)

Q: 17. If the curve C is given by x= 3t² +1, y=4t, z = e, find the equation of the tangent line at the…

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Q: Find y' and the slope of the tangent line to the graph of (3x-2y)5 = 2y2-9 at the point (1,2). y'=0…

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Q: The curve y = ax2 + bx + c passes through the point (1, 2) and is tangent to the line y = x at the…

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Q: a) Find an equation of the tangent line: x' +y' + 9xy = 27 at (x, y) = (1, 2)

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Q: The equation of the tangent line to the curve at the given point. x2 v2 2-13 = (1, 1) is %3D 100 4…

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Q: 5 Find the equation of line tangent to the curve y= x+ y at point P(1,3) A 4x - y - 7 = 0 B None of…

A: Given that: y=x+5x

Q: Find the equation of the tangent line to the curve (a lemniscate) 2 2(a? + y?) = 25(æ² – y²) at the…

A: Topic:- application of derivatives

Q: The equation of the tangent line to the curve x² + y? = 25, at (8,-12) is 12 O y = ++ 8) – 12 8 8 O…

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Q: The families of curves represented by the solution of the equation dy dx for n = - 1 and n = + 1,…

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Q: 5 Find the equation of line tangent to the curve y= x+ at point P(1,3) A None of the given choices…

A: Given curve is y=x+5/x and Point=P(1,3)

Q: a) Given a curve y = px* + 2x has turning point at (–1,q). Find the value of p and q.

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Q: a. Determine the points where the curve 4x + 5y - y = 6 has a vertical tangent line. b. Does the…

A: a)  curve is 4x+5y2-y=6         Slope of tangent line is m=dydx    Differentiate the above equation…

Q: a. Verify that the given point lies on the curve. b. Determine an equation of the line tangent to…

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Q: Find the equation of a line normal to the curve of y= cos at x= 1. Select one: A. -33 x + 9y - 9 +…

A: Equation of Normal

Q: Determine an equation of the tangent line to y = (e +2)ª at the point (0, 81), then solve it for y.…

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Q: The curve y = ax + bx +c passes through the point (1,9) and is tangent to the line y = 4x at the…

A: Please see the answer below.

Q: The curve y = ax + bx +c passes through the point (1,4) and is tangent to the line y = 3x at the…

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Q: (a) Find an equation of the curve that has slope (xy²- x2) dx + (3x²y² + x²y - 2x3 + y?) dy = 0 %3D…

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Q: Find the equation of line tangent to the curve y= x+ - at point P(1,3) A 4x + y - 7 = 0 В) 4х - у -7…

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Q: Find an equation of the tangent to the curve at the given point. (1) X²+4xy-y²-4x=1, (1,2) (2)…

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Q: A heat-seeking particle has the property that at any point (x, y) in the plane, it moves in the…

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Q: The x- coordinate of the point on the graph of y = Vx-1 at which the tangent line is perpendicular…

A: slope of tangent of the curve y=x-1 is dydx=12x-1 slope at (x1, y1)dydx=12x1-1=m1if (x1, y1) is the…

Q: If a curve f(x) has dx dy = (y – 1)2(2+ x) and passes through the point (-1,2), then what is the…

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Q: a. Verify that the given point lies on the curve. b. Determine an equation of the line tangent to…

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Q: 20. Find the equation of the curve for which y" =x, and which passes through the point (1, 2) and…

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Q: If the length of the curve y = 4 x7 from the point (0, 0) to the point (Xo, f(xo)) is L= 1 (145)*…

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Q: Find the values of a and b for the curve x2 y + ay2= b if the point (1,1) is on its graph and the…

A: Find the slope of tangent line

Q: The curve y= ax² + bx +c passes through the point (1,2) and is tangent to the line y = x at the…

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Q: The tangent line to the graph of y = In(x² – 1) is perpendicular to the line a + y = -1 at the point…

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Q: 4) Given :y = ax + bx +1, the curve touches the line x+ y = 0 at %3D The point (3,-3). Find the…

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Q: 16. The slope of the tangent line at any point (x, y) on the curve is 3x2 - 2x +7. What is the…

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Q: 20. Find the equation of the curve for which y" = x, and which through the point (1, 2) and the…

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Q: (a) Find the slope of the line tangent to the curve y = sin x at the point where x = T/3. (b) Show…

A: (a) we have to  find the slope of the tangent line to the curve y=sin5x at the point where x=π3. as…

Q: The tangent line to the curve y=vx-5 * for x=16 is a. y=1/8 (x+16). O b. y-4=1/6 (x-16). O c.…

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Q: Find the values of a and b for the curve x2y +ay2 = b if the point (2, 2) is on its graph and the…

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Q: The slope of the tangent line at any point (x, y) on a curve is 2A If the point (9, 3) is on the…

A: we can obtain the equation of curve by forming a differential equation . we know that the slope of…

Q: a. Determine the points where the curve 4x + 2y -y =1 has a vertical tangent line. b. Does the curve…

A: Consider the given curve 4x + 2y2 – y = 1