3. Consider y= r+ y. Draw the isocline for the equation that corresponds to y = 1 and then draw ten tangent segments on this isocline that are in the slope field for y x+ y. Now draw five more tangent segments that help to estimate the solution to the IVP / =x+y* if y(1) = 0. Show points used to calculate the slopes. 3. -1 -1 -2 -5

Q: 14. What is the slope of the curve at the point (0, x²+y-12r +4y = 5 %3D 0-2

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

A:

Q: 2. Ali is seated on the line which is normal to the curve f(x) = x² - 2x + 4 at the point (1, 3). 3.…

A: As per the company rule, we are supposed to solve the first three sub-parts of a multi-part problem.…

Q: Find the length of the curve on y=2x^(3/2) from x=0 to x=1

A: Explanation of the solution is given below...

Q: (b) Find a , b and c if the curvey = x + a x + b and y =c x + x have tangent lines paralle to each…

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Q: (b) Compute the slope of the line that is parallel to the xz-plane and tangent to the surface z = x…

A: Given: Let's calculate the slope of the line tangent to the surface z=x(x+y) at the point that is…

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Q: If y=mx+b is the equation of the tangent line the curve y = x- 3x +5, which is parallel to the…

A: We will solve the problem

Q: 18,8grt(10)) 10 f(x) = V2x – 2 compute the instantaneous slope at: (6, v10) Start with two points A:…

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Q: The direction field of the DE y' + ye³x+7 = −2y² will have a line segment with positive slope at the…

A: Given y'+ye^(3x+7)=-2y² We know that the dy/dx gives the direction field. Hence the given DE can be…

Q: The slope of the tangent line to the parabola y = 2x + 2x + 6 at the point (- 1, 6) is: The equation…

A: The slope of the tangent line to the parabola                      y = 2x2 + 2x + 6 at the point…

Q: 1. Differentiate Y in terms of X in x^3 + x^2 + 4xy - 2y +5y^2 = 10 2. Determine the slope of the…

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Q: An object is traveling along the line y = 2x + 1 heading up and to the right. If the temperature at…

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Q: Determine a, b, c and d so that the curve y = ax^3 + bx^2 + cx + d will have a critical point at the…

A:

Q: The slope of the tangent line to the parabola y = 2x“ + 2x + 6 at the point (1, 10) is: The equation…

A: Given,            The parabola is y=2x2+2x+6 and the point is 1,10.

Q: At what point on the curve x = 6t2 + 5, y = t3 − 1 does the tangent line have slope of 1/2?

A: We can use application of derivative in order to solve the given problem.

Q: Find an equation of the parabola y = ax2 + bx + c that passes through (0, 1) and is tangent to the…

A: Given" Parabola y = ax2 + bx + c that passes through (0, 1) and is tangent to the line y = x − 1 at…

Q: FInd c so that the curve y = x3+ cx2+67 will have a relative extrema at (2,5). Find other extreama…

A: Consider the equation of the curve, y=x3+cx2+67 Solve for the stationary points as,…

Q: Find an equation of the parabola y = ax2 + bx + c that passes through (0,1) and is tangent to the…

A: Since, the parabola passes through (0,1) ,so,we substitute x=0, y=1 ,to get c=1

Q: Show that no point on the graph of x 2 - 3xy + y 2 = 1 has a horizontal tangent line.

A: Given  x 2 - 3xy + y 2 = 1

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

A: To determine the x-intercept of the curve and slope of the tangent at the intercept.

Q: Obtain a slope field and add to it graphs of the solution curves passing through the given points.

A: The given differential equation is y'=xyx2+4. Sketch the slope field and its solution curves that…

Q: Find the member of the curve whose slope at any point is 2e** and passes through the point (0, 1)

A: We need to find the member of the curve whose slope at any point is 2e^(4x) and passes through…

Q: 2 Find the point onthe curve y=Jx that is. the point (4,0). minimum distance from a

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Q: The slope of the curve 2y = ax + b at (1,-1)is -1.Find a, b.

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Q: A farmer calls in from his home 12.5 km from the eruption site to report that 15.5 mm of ash fell on…

A: From the curve we find that the predicted Ash fall for 12.5 away from home is 8 mm.…

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: What is the slope of the tangent line that touches the graph of In(y)+e2x-=3y – 4x at the point (A 1…

A: The solution are next step

Q: 2 Show that the line y = x +3x+m for all values of m. y= mx+4 will touch or intersect the curve

A:

Q: FInd c and d so that the curve y = x3+ cx2+d will have a relative extrema at (2,5). Find other…

A: Given y=x3+cx2+d

Q: 4. Find the two values of a for which the line connecting the point (1, –1) to a point (a, a²) on…

A:

Q: The equation of the curve in the tx-plane which passes through the point (2,3), and has, at every…

A: In this question, slope of curve and point is given and we have to find out equation of cuve.

Q: obtain a slope field and add to it graphs of the solution curves passing through the given points.…

A:

Q: 3. The cost C of manufacturing transformers in a factory varies with the output N per day according…

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Q: What is the sum of the abscissas of the points where the tangents of the y=(1/3) x^3-(3/2) x^2 – 2x…

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Q: -4 The number of tangents to the curve of y=- x³ + 6x? which have a slope of 8 is:

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Q: Find the values of a and b if the tangent to y = ar² + bx at (1,5) has a slope of 8.

A:

Q: If the curve is defined by y= x⁴ - 8x³ + 22x²-24x+9, then what are the value/s of x for which the…

A:

Q: Obtain a slope field and add to it graphs of the solution curves passing through the given points.…

A: The point is given as x0 , y0 The slope is given by value of dydx at y = y0 Also the equation of…

Q: A tangent line to the curve c(t) - (- 4t - 5t + 2, t - 15t - 1) has slope 3 at the pointias) 2-1…

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Q: 17. The line with equation y = 2x b where bis a constant, passes through the point (3, 6). What is…

A: When a line passes through a point then the coordinate  values of the point must satisfy the…

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

A:

Q: Find an equation of the parabola y = ax² + bx + c that passes through (0, 1) and is tangent to the…

A:

Q: Suppose the curve y =x4 +ax3+ bx2+ cx +d has atangent line when x=0  with equation y= 2x +1 and…

A: Given the curve is   y =x4 +ax3+ bx2+ cx +d Differentiating with respect to "x" y' = 4x3 + 3ax2 +…

Q: FInd c and d so that the curve y = x3+ cx2+d will have a relative extrema at (2,5). Find other…

A: Maxima or minima: Let f(x) is any function. 1) Evaluate f'(x) = 0 for critical point. 2) Evaluate…

Q: 1) Find the slope of the line tangent to the graph of y=x²+1at(2, 5).

A:

Q: obtain a slope field, and add to it graphs of thesolution curves passing through the given points.…

A: We have to find the slope field and add to it graphs of the solution curves passing through the…

Q: 10. At what point on the parabola y = 3x² + 2x is the tangent line parallel to the line 10x – 2? y

A: Given,          The parabola y=3x2+2x is the tangent line parallel to the line y=10x-2.

Q: At what point on the curve x = 6t2 + 2, y = t3 - 5 does the tangent line have slope (x, y) =

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Q: obtain a slope field and add to it graphs of the solution curves passing through the given points.…

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.