Find an equation of the curve that passes through the point and has the given slope. (Enter your solution as an equation.) (0, 4), y' = 14y

Q: Find an equation of the line tangent to the curve defined by z2 + 6ry +y = 32 at the point (2, 2).

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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: Find the slope of the line tangent to the curve at the given point. y = 7 cos x ; x = 4 C. - 7V2 7V2…

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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: Find the differential equation of the family of circles having their centers on the y-axis. With an…

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Q: 4. Find y'(x) for x²y² – 2x = 4 – 4y. Then find the equation of the tangent line at (2, –2 _n…

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Q: 2. Find the slope of the tangent line to the curve y = 4x² – 2 at x= 1. What is the equation of the…

A: The given curve is y=4x2-2. At x=1, y=412-2=2. Thus, the graph is passing through 1, 2. The slope of…

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: 15. Find the equation of the curve whose slope at any point is equal to -(y +1)/(x + 1) and which…

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Q: Find the equation of the curve that passes through the point (1, 3) and has a slope of y/x2 at any…

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Q: Find an equation of the line tangent to the curve xy + 4y = 68 at the point (1,16). An equation of…

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Q: Find an equation of the curve that passes through the point (0, -7) and whose slope at the point 2x…

A: we have to find the equation of the curve

Q: 3. Find equation of the curve whose slope at any point is equal to 1– and which Inx x In x passes…

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Q: (b) Find the equation of the tangent line to the curve 8x²y3 – 5x? + 7y³ = 10(x – 3y), at the point…

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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: Find an equation of the curve that passes through the point (3, 1), and has the given slope y′ = −…

A: Given that y'=-y5xdydx=-y5x

Q: The function y(x) is given implicitly by the equation y3−3xy+x3=3. Find its differential at the…

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Q: Find the slope of a line tangent to the curve of the given equation at the given point. y = x2 - 3;…

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Q: 1. Find an equation of the tangent line to the curve y = 2x3 – 5 at the point (-1,3).

A: As per our guidelines we are supposed to answer only one question.Kindly repost other question as…

Q: Find the equation of the line tangent to the graph of x3 + y3 = -5xy + 7 at (1,1).  The equation of…

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Q: Find the equation of the curve that passes through the point (0, 2) and has a slope of at any point…

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Q: A particle is moving along a line in such a way that v centimeters per second is the velocity of the…

A: A particle is moving along a line in such a way that v centimeters per second is the velocity of the…

Q: find the equation of the line tangent to the curve y=x^4-4x^3+2x^2-4x+15 and perpendicular to the…

A: To find the line tangent of the curve we have to differentiate with respect to x. If first-line…

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

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Q: Find an equation of the curve that passes through the point (0, 2), and has the given slope y′ =…

A: y'=x4y, (0,2) Formula ∫xndx=xn+1n+1+C

Q: Find an equation of the curve that passes through the point (1, 1), and has the given slope y′ = −…

A: y'=-9x16yPasses through (1,1)Formula∫xndx=xn+1n+1+C

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 an equation of the curve that passes through the point (0, 6) and whOse slope at (X, y) is X/y.

A: Given that: Slope of the curve at (x, y)=xy

Q: find an equation of a straight line tangent to the curve y=e^x and passing (0,0).

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Q: Find the equation of the tangent line to the curve (a lemniscate) 2(x² + y²)² = 25(x² – y?) at the…

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Q: Find an equation of the curve that passes through the point (0, 2) and whose slope at (x, y) is x/y.

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Q: The slope of the curve y^2-xy-3x=1 at the point (0,-1)

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Q: 2. Find the equation of the tangent lines and the normal lines to the curve y = 2x² +3 at the point…

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Q: Find an equation of the curve that passes through the point (0, 4) and whose slope at (x, y) is x/y.

A: Solution:find the equation of curuepasses through the point (0,4)slope of cwue is xydydx=xyy dy=x…

Q: 9. Find an equation of the line tangent to the curve y = 2x - 7x2 + 10 at the point (3, 1). y = 12

A: Given that, the curve is y = 2x2 - 7x2 + 10  To find the tangent line to curve at point (3,1)   To…

Q: 1. Find the equations of tangent and normal lines to the curve whose equation y2 – 6x2 + 4y + 19 = 0…

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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: The equation of the tangent to the curve y = x – 3x² – 2x + 2 at the point where the curve cuts the…

A: We have to find  the equation of tangent in the form of y=mx+c.

Q: 15. Find the equation of the curve whose slope at any point is equal to -(y + 1)/(x +1) and which…

A: We have to find the equation of line when given slope and passing through the point

Q: Find an equation of the curve that passes through thepoint (0, 1)and whose slope at (x, y) is xy.

A: To Determine: Find an equation of the curve that passes through the point (0, 1)and whose slope at…

Q: A heat-seeking particle is located at the point (2,3) on a flat metal plate whose temperature at a…

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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 slope of the curve, equations of the tangent and normal lines to the given point. y = x3 –…

A: We have to solve the problem

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

Q: Find the equation of the line tangent to the graph of 2 + y* = - 2xy + 13 at ( – 3, 4). The equation…

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Q: Find an equation for the tangent line of y = e* that is parallel to the linear equation y = 5x + 17.…

A: Given y=e8x let at point  (h,k) on curve y=e8x tangent is parallel to the  y=5x+17

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.