1. Find the equation of the family of curves and the equation of the particular curve that passes through point (-2,-5) if the slope of the tangent at any point (x, y) is a. 3x + 4 x+2 b. 1- y

Q: find y' and the slope of the tangent line to the graph of  (3x - 2y)^7 = 2y^2 - 9 at the point…

A: The given equation is- 3x-2y7=2y2-9 Since, y' =dydx is the slope of the tangent line, Then…

Q: 7. Find the slope of the tangent line to the graph at (1,1): x²y² – 9x² – 4y² = 0 %3D r-9r-4y = 0…

A: find the slope of the tangent line to the graph at 1,1; x2y2-9x2-4y2=0 differentiate the equation…

Q: [3] If the curve is defined by y = x* – 8x3 + 22x2-24x+9, then what are the value/s of x for which…

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Q: Find the equation of the curve that passes through the point (1, 3) and has a slope of at any point…

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Q: Find the equation of a line normal to the graph of y = 3x+5/x−1 at x = 3

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Q: Find the points at which the graph of this equations has vertical or horizontal tangent lines:…

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Q: Find an equation of the tangent line to the graph at the given point. (y - 3)2 = 4(x- 5), (9, 7) %3D…

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Q: Find an equation of the tangent line to the graph 16x4 + y4 = 32 at the point (1,2). %3D 1) 5 1 -+x-…

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Q: Find the equations of the tangent and normal line to the following curves at an indicated points:…

A: 1). Given curve is y=2x2-5. To find the equations of the tangent and normal line at point 2,3.…

Q: 8. What is the slope of the line tangent to the curve defined below at the point (1,1)? 1 -1 -2

A: The solution are next step

Q: Find the equation of one of the tangent lines to the circle x^2 + y^2 = 5^2 that passes through the…

A: Here, to find the equation of the tangent line to the circle  x2+y2=52⇒x2+y2=25...(1) that passes…

Q: Find an equation of the tangent line to the curve at the given point.y=8x-6x^(2), P(4,-8)

A: y=8x-6x^(2), P(4,-8)Let the equation of the tangent: y=mx+cSlope of the tangent =m =  dy/dx.

Q: 1. Find the equation of the lines tangent and normal to the curve 3x?y2=4x2-4xy. at the point…

A: Since you have asked  multiple questions in single request  so we  will be answering only first…

Q: Find an equation of the tangent line to the graph at the given point. 3(x² + y2}² = 100(x? – y²),…

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Q: B. Find the slope and the equation of the tangent line to the curve 1. y = 4 - 3x at (- 1, 1) 2. y…

A: We need to find the slope and the equation of the tangent line tothe following curve:3. y=3x2+2 at…

Q: 4. At what point on the graph of y = ÷x² is the tangent line parallel to the line 2x – 4y = 3? A.…

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Q: Find the equation of the tangent line to the graph of a+ y = 3 at the point (1,4). 1) y - 4 = 2(x -…

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Q: For the curve y = ax + bx2 + 12x - 7, what values of a and b will make the tangents to the curve at…

A: we have to solve the problem

Q: Find an equation of the tangent line to the graph at the given point. (x + 2)2 + (y – 3)² = 37, (-1,…

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Q: 6. Find the member of the curve whose slope at any point is √y and passes through the point (2, 1)

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Q: 10. Find the slope-intercept form of the equation of the line tangent to the graph of y arctan(9x)…

A: Given y = arc tan9xand x=39here we find the slope - intercept form of the equation of the line…

Q: Find the equation of the tangent line to the graph of y = 2x - (4 / √x) at the point (4, 6).

A: Given,            y = 2x - 4x and Point is 4, 6

Q: Therefore, the curve y = x* - 2x2 + 2 has horizontal tangents at x-0, 1, and -1

A: Just compute the derivative and equate it to zero.

Q: , If the curves yı = -x² + ax +b and y2 x² + cx - 2 have the common tangent line at the point P(1,2)…

A: Given information: There are two equations  are y1=-x2+ax+b, y2=x2+cx-2 have a common tangent line…

Q: 1) Find the slope of the tangent lines on the curve y = 6x + 24x -39x - 43 at points | (-5,2) and…

A: Slope of line is given by m = dy/dx = tan θ y = 6x3 + 24x2 - 39x - 43  Differentiating with respect…

Q: Find y′and the slope of the tangent line to the graph of ​(2x-5y) 5=4y2 -3 at the point ​(3​,1​).

A: Find y′and the slope of the tangent line to the graph of ​(2x-5y) 5=4y2 -3 at the point ​(3​,1​).…

Q: 1 5 Determine the equation of every tangent to the curve y = =x° - 10x that has a slope of 6

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Q: 3. Find the equation of the curve at every point of which the tangent line has a slope of 4.x. (a) y…

A: Topic = Differential equation Correct option = d

Q: The family of curves orthogonal to ye2x = c is the family of curves whose general equation is?

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Q: Find the equation of the family of curves whose slope at any point (x,y) is given and which passes…

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Q: 2. Find the equation of the line that is tangent to the circle x + y = 25 at the point P(3,4)

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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: 9. Find the points on the graph y = 7x - where the slope of the tangent line is parallel to x-2 28x…

A: To find- Find the points on the graph y = 7xx - 2 where the slope of the tangent line is parallel to…

Q: 6. Find an equation in the form y = ax³ + bx² + cx + d__whose graph has an x-intercept at x = -1, a…

A: Given: x-intercept at  y = 2 y-intercept at x = -1 slope at (-2,-2) is 5. (-2,-2) lies on the curve…

Q: The points at which the graph of the equation 8x2+ y² – 16x + 8y + 8=0 has horizontal tangent lines…

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Q: 1 - Find the equation of the tangent line to the curve y = 3 5 x2 +6x 2 11 at its point of…

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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: Find an equation of the tangent line to the graph at the given point. (x + 2)2 + (y – 3)² = 37, (-1,…

A: We have to find equation of tangent line to the graph of function: x+22+y-32=37 at -1, 9 We know…

Q: 5. Find the point on the parabola y=-x+3x+4 where the slope of the tangent line is 5.

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Q: What is the slope of the tangent line that touches the graph of In(y) + eA-=3y-4x at the point 3. 5

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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: Find the two points where the curve x2 + xy + y2 = 7 crosses the x-axis, and show that the tangent…

A: To find the x-intercept we plug y=0

Q: Find the equation of the family of curves whose slope at any point (x,y) is given and which passes…

A: To find the equation of family of curves whose slope is given .

Q: 15.)) What is the slope of the line tangent to the curve y +2 = - 2sin y at the point (2, 0)? 2 (A)…

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Q: At what point on the graph of y = (x^2)/2 is the tangent line parallel to the line 2x - 4y = 3? O…

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Q: Find the values of a and b for the curve x²y+ay²=b if the point (1,1) is on its graph and the…

A: It is given that, x2y+ay2=b   ...(1)and4x+3y=7    ...(2) Here equation 2 represent a tangent line…

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: B. find the slope of the tangent to the curve at the given point 1. y= x-6, (1, - 2) 2. y = 3x -5x.…

A:

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.