(a) Find an equation of the curve that has slope (xy²- x2) dx + (3x²y² + x²y - 2x3 + y?) dy = 0 %3D and passes through the point (0, 0).

Q: Find the equation of the curve that passes through (0, 9) if its slope is given by dy/dx = 12x^2 −…

A: We can find the equation of the curve by integrating the given derivative and substitute the point…

Q: 34. Find the slope of the curve x^2 - 3xy y^2 - 4x + 2y + 1 = 0 at the point (1,-1 O 1/5 1/6 O 1/4 O…

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Q: 1 ) Find the equation of the curve for which   y” =  6x – 4 and which passes through (1,2) and (-2…

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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: use the method in Example 3 to find (a) the slope of the curve at the given point P, and (b) an…

A: y=x2-2x-3

Q: 6. Find the point on the curve y = yx that is closest to the point (3, 0)

A: let P is the closest point then say (x,y) then find the distance from the point (3,0)  then minimize…

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

A: We have to find equation of tangent and normal

Q: X- S- V3e2x - 2e-2x dx VZe-2x+ /2e-4x - 3 +C 2/2 2/3e2x - 2e-2x + C V2e-2x +C 1 -Arcsin 2 V3 -Arcsin…

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Q: ind the equation of the line tangent to the curve 3x² + 16y² = 192 at the point Mx + K. P= (-4, 3)…

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Q: An equation of the line tangent to the graph of f(x) = x(1-2x)3 at the point (1,-1) is A. y = -7x+ 6…

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

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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: h (x) = [ƒ (x)P + g (x), what is the equation of the line tangent to the graph of h at x=-1?

A: Given,           hx=fx2+gx

Q: find an equation of the curve that satisfies (dy)/(dx)=45 yx^14 and whose y-intercept is 2 y(x) =

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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: find the equation of the line tangent to the curve at the given point x2y2=4y ;(2,1)

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Q: 2x Find the equation of the line tangent to the graph of y= In(3x)+- at x=1 6

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Q: use the method in Example 3 to find (a) the slope of the curve at the given point P, and (b) an…

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Q: 3. Find the slope m of the tangent lines to the parabola y = -x+ 5x+ 6t its point of intersection…

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Q: Find the equation of the tangent to the curve x3 + y3 = 9 at the point (1,2). a. 3y-x-5=0 b.…

A: As we know that; The equation of the tangent line passes through the point Px0,y0 is: y-y0=mx-x0…

Q: dy = 18yx³ dx and whose y-intercept is 4. y(x) =

A: A detailed solution is given below

Q: 1 Find the points at which the graph of the equation 4? + y² – 8x + 4y + 4 0 has a vertical or…

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Q: Which is the equation of the tangent line to the curve x +xy = 4+ y² at the point (4,6)? a) y-6=3(x-…

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Q: 1 Find an equation of the tangent to the curve f(x) = /x + 8 that has slope 4 %3D - OA. 1 y =7x-3 O…

A: Equation of the line in slope-point form is:        m = slope (x1, y1) = point on the line

Q: 6. Find the equation of the curve whose slope at any point (x,y) is xy and which passes through the…

A: 6. We know that the slope of the function is defined as dydx given that xy Therefore, dydx=xy or…

Q: Find an equation for the tangent to the curve at the given point. y = x2- 3, (-4, 13) Oy = -4x- 19…

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Q: Find the particular solution of the linear equation dy/dx+y/x= x if y(1) = 0.

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Q: This is the equation of the line tangent to the graph of * y = x2 + 3 at x = –1

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Q: The point (2,1) is on the graph of x2 . y3 + 5· x² = y² + 23. Find the slope of the line tangent to…

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Q: 2) Find the equation of the curve whose slope at any point p(x,y) is m =x (x +5)² and passing…

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Q: 12. Find an equation of the tangent line to the parabola y = x2 – 1 at the point (2 ,3 ).

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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: x² - y² + xy dy/dx =0  What is the general solution of differantial equation

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Q: s) Find the equation of the curve that passes through the point (3, 2) if its slope is giv dy = 8x –…

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Q: Find the equation of the line tangent to y = 3x² + x +1 at x = -3 Oy=-17x - 26 Oy=6x-3 Oy=-17x - 3…

A: Given that y=3x2+x+1, x=3 We know that the equation of the tangent is y-y1=mx-x1 where m is the…

Q: 1. Find the equation of a curve that passes through the origin and satisfies (1 + x²)y' + 2xy = 4x²

A: Given differential equation is  1+x2dydx+2xy=4x2 Simplify the given differential equation we get…

Q: Find y in terms of x. dy dx 12x(3x 2 - 1)3, curve passes through (1, -3) A y= (3x 2.1) 4 B y = (3x 2…

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Q: 1. Find the equation of a curve that passes through the origin and satisfies (1+x²)y' + 2xy 4x2

A: To find the equation of the curve

Q: Find an equation of the curve that satisfies dy/dx = 150yx14   and whose y-intercept is 2.   y(x) =…

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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: Find the points at which the graph of the equation has a vertical or horizontal tangent line. 16x2 +…

A: Solution of given question is written in below steps.

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: 6. Consider the curve 5x - xy + y =7. The slope of the line tangent to the curve at the point (1,2)…

A: To find the slope of the line tangent at the point (1,2) is substituting the point in the dy/dx . We…

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: Find an equation for the tangent to the curve at y =x2 + 1, (4, 17) y = -4x - 15 O y = -8x - 15 y =…

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Q: An equation of the line tangent to the graph,of f (x) = x(1– 2.x)' at the point (1,–1) is D y = 7x…

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Q: h(x) * |4x + 1 %3D a) Find the equation of the line tangent to the graph of fx) at x = 2.

A: 8). Given function is hx=4x+1. To find: (a). The equation of the line tangent to the graph of fx at…

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

A: Differentiation and find slope and use formula