Obtain the differential equation of the family of plane curves described and sketch several representative members of the family. 1. Straight lines through the fixed point (h, k). Ans. (y -k)dx-(x-h)dy= 0 2. Straight lines with slope and x-intercept equal. Ans. (y’)^2 = xy'- y

Q: The slope of the tangent line at any point (x, y) on the curve is given by (x + 2) + 1.lf the curve…

A: Let the given curve be y=fx.Given that dydx=x+223+1Also, it has an x-intercept of -2, that means,…

Q: Given y+xcos y = cosx. (i) Name a suitable technique to find the derivative of the (ii) Find dx dy…

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Q: 16 The point P(1, 0) lies on the curve y = sin( (a) If Q is the point (x, sin(16)), , find the slope…

A: Given: Let us consider the given point P1,0 lies on the curve y=sin16πx. The point Qx,sin16πx Lets…

Q: 6. Find the equation of the tangent line and the equation of the perpendicular line to the curves at…

A: By applying the applications  of derivative concepts we will find slope of the tangents to the…

Q: Using the function y = 4x3 + 6x2 – 5x + 3, find y"(3). a. 84 b. 24x + 12 C. 60 d. 72

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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: 41–44. Tangent lines Find an equation of the line tangent to the following curves at the given…

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: 5. Find the slopes of the tangent lines to 2x? – 3xy+y³ = -1 at y = - 3.

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Q: Let f (x) = (x³ –- 2x + 2)° Lans(1) = (x' – 2x + 2)' ma g(x) = 5" (x) and 8 (x) = f¯l (x). What is…

A: The slope of the curve g(x) at a point will be the derivative of the function, g'(x) at that point.

Q: Which of the following would represent the equation of the graph that passes through the point (8,…

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Q: Find an equation of the tangent line to the curve at the given point. y = (x - 1)/(x - 2), (3, 2)

A: Equation of line passing through and whose slope is m is given as

Q: Find the leguation tor the tangent to the at the point (1ら3). Curve y=x+3

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