If dy = dz, what is the equation of y in terms of x if the curve passes through (1, 1)? General Solution (equate y in terms of x) Particular solution (equate to zero) Value of the constant, C

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: An equation of the tangent line to a curve at the point (2, 4) is y = x + 2. if at any point (x, y)…

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Q: 5. Given the parabola y = - x? + 10x - 16 and two tangents that pass through (4, 12), find the slope…

A: A general equation is taken and then it is molded as per the conditions.

Q: 16. John tries to find the equation of the tangent line to the graph y=5x+1 at x=2. His calculations…

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Q: The graph of the implicit equation x2+3xv+4v² = 1 is shown here with lines indicating where the…

A: In this question, we find the point of intersection with the curve and horizontal tangent to the…

Q: Solve for C given the general functions below and the specific point. 9. Find the equation of the…

A: Since:              The given general equation is of the form:…

Q: 7. An equation of the line tangent to the graph of ƒ at the point (2, 7)is y = 4x - 1. Find ƒ(2) and…

A: Given function is fxequation of the tangent line y=4x-1tangent of the graph 'f'=dfdx=y=4x-1  ∴…

Q: 2(x² + y? )² = 25(x² – y²) at the point (3, 1). When the equation of this tangent line is written in…

A: Given that 2(x^2+y^2)^2=25(x^2-y^2) To find the equation of the tangent line

Q: 2. +y = (1 + 3x)r

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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: Two objects moving along x-axis are starting at the same time. Their positions are measured in…

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Q: 5) The circle defined by the equation x + y = 18 has two points where the slope of its tangent line…

A: As per the guidelines, we are supposed to answer only one question at once. Kindly repost the other…

Q: The curve defined by the equation: x^(2/3) + y^(2/3) = 1 is an example of an astroid (shown…

A: To find the points on which the slope of tangent line is -1

Q: An equation of the tangent line to a curve at the point (3, 5) is y = x + 2. if at any point (x, y)…

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Q: Two objects moving along x-axis are starting at the same time. Their positions are measured in…

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Q: Find an equation of the line tangent to the graph of G(x)=5 eX at the point (0,5). The equation of…

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Q: The non-homogenous solution of the following equation by using variation of parameter method y" +y =…

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Q: The equation x² + y² = (2x² + 2y² – x)² describes a cardioid: a. Find an expression for in terms of…

A: x2+y2=2x2+2y2-x2 a). Differentiating with respect to x, we get…

Q: 15 Given a tangent line to the curve y=x-2x is perpendicular to the straight line 7 23 Find the…

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Q: A curve has an equation of y = x3 - 6x2 + 9x + 2. Find the point of inflection of the curve. а. (2,…

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Q: Q3 The length of a curve from (0 ,-3) to ( 3,3)is given by Vx4 – 2x2 + 2 dx Which of the following…

A: Length of curve

Q: Find the equation of the line tangent to the curve y= x^3 + 5x at the point (1,6) Include y = in the…

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Q: Find the equations of all lines through the origin that are tangent to the curve y = x³ – 4x? – 4x.…

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Q: The tangent line to the curve at the point (1,2) also passes through d²y the point (-1,4). If at any…

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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: max(-x - xy-2y + 2rx + where r is a parameter. Verify equation (3). SM 5. Find the solutions x* (r,…

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Q: A curve has equation 2x3 4x²y + 3y2 = 3. - dy Find the value of at the point (2, 1). dx

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Q: 8. A curve whose slope at any point is 6x² А. у %3D 2х3 — х? +х+6 - 2x + 1 passes through the point…

A: We need to find equation of curve.

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

A: Given, The curve  y=ax3+bx2+12x-7 We have to find the value of a  and b such that tangent to the…

Q: Find an equation of the tangent line to the function y= 4x at the point P(1, 4). Solution We will be…

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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: Two objects moving along x-axis are starting at the same time. Their positions are measured in…

A: To find the distance between objects.

Q: 2. The length of a curve from x =1 to x = 4 is given by V1+9x* dx. If the curve contains the point…

A: For              y=f(x)        , a≤x≤blength of the curve= ∫ab1+dy2dx2.dxor arc length…

Q: parabola y = x2 - 6x + 7 at the point (2, -1). SOLUTION From the previous example, we know the…

A: Given query is to find the equation of the tangent line on f(x).

Q: The curve y = f(x) has a y – intercept of 3. The tangent to this curve at the point (x, y) has an x…

A: Given that the curve y=f(x) has a y-intercept of 3.  That means y(0)=3. also given that the tangent…

Q: Two objects moving along x-axis are starting at the same time. Their positions are measured in…

A: Given  s1= 2t2-3t             s2=3t-t2

Q: 4) Given the equation x3 + y3 = 9x (implicit), find y'. Then find the slope and equation of the…

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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: 2(x² + y? )° = 25(x² – y}) at the point (3, 1). When the equation of this tangent line is written in…

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Q: Two objects moving along x-axis are starting at the same time. Their positions are measured in…

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Q: A curve having an equation y = ax? + bx2+ Cx + d has a critical point at the origin and a point of…

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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: 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: Two objects moving along x-axis are starting at the same time. Their positions are measured in…

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Q: Two objects moving along x-axis are starting at the same time. Their positions are measured in…

A: Distance

Q: A point moves along the curve y = 2x 3 − 5x 2 − 1 (cm). (a) Find the direction of travel at x =…

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Q: Discuss the properties of the curve (w/ solution) and sketch fully: 1+lnx y =

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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: A curve is defined by the equation 2sin(y) – xy + y2 = 0. (a) Verify that the curve passes through…

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