Solve step by step please Draw the level curves of f (x,y) = C indicated for each choice of C f (x, y) = In(x² + y²), C = 4, C = In4

Q: Find the points on the curve  y = x3 + 3x2 − 9x + 2 where the tangent is horizontal.   smaller…

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Q: Select equations for level curves of the function f(x, y) = x-³y in the following order: f(x, y) = ,…

A: Given : f(x,y) =x-3y Order : f(x,y) =1/4 f(x,y) = 1  f(x,y) = 4

Q: Two curves are orthogonal if their tangents are perpendicular at each point of intersection. Show…

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Q: A differentiable function has the value y(2) = 1 and the derivative value y'(2) = 3. Approximate the…

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Q: Find the maximum rate of change of the function f(x,y) = sin(xy) at the point (0,1) and the…

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Q: 28. The line tangent to the graph of g at the point (x, y) inter- sects the x-axis at the point…

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Q: 66) The curve y = ax2. point (2, 28) and is tangent to the line y 2x at the origin. Find a, b, and…

A: We know that,The slope of a curve y = f(x) is given by m, where m is

Q: (b) Apply the First Derivative Test to identify the relative extrema. (x, y) = ( ,1 2 relative…

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Q: Find the points of inflection of the curve y = (1 + x)/(1 + x²). (Hint: All three lie on one…

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Q: The temperature is T(x,y) degrees at any point of a rectangular plate lying in the xy-plane and T(x,…

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Q: FInd a so that the curve y = x3+ ax2+ 44 will have a relative extrema at (2,5). Find other extrema…

A: The given curve is y=x3+ax2+44. Since the curve has a relative extrema at (2,5), x=2 is a critical…

Q: Examine the function for relative extrema and saddle points. (If an answer does not exist, enter…

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Q: The tangent line to the graph of y = g(x) at the point (4, 5) passes through the point (7, 0). Find…

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Q: How many tangent lines to the curve y = x / (x + 5) pass through the point (1, 2)? At which points…

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Q: Find all points (if any) of vertical tangency for the curve represented by x=r +2t –3 and y =r² –…

A: Topic- tangent to the curve

Q: Find all points where the functions have any relative extrema. Identify any saddle points.ƒ(x, y) =…

A: Consider the function:  fx,y=x2+xy-2x-2y+2. Find the points of relative extrema identify saddle…

Q: Find the 1st order derivative for    R(x,y) = [(x^2)/(y^2 + 1) ]  -   [(y^2)/(x^2  + y)]

A: Given function is R(x,y)=x2y2+1-y2x2+y Differentiate partially with respect to x.…

Q: Find the cubic function y = ax3 + bx2 + cx+ d where its graph has horizontal tangent line at (-2,6)…

A: I have written the important facts in the solution part

Q: Find the equation of the tangent line in the given place. complete solution 1.) Tangent to the…

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Q: Find all points (x, y) on the graph of f(x) = x? with tangent lines passing through the point (3,…

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Q: := cos z + sin y, –T/2 < x < a/2, –x < y < a b) Find relative max / min / saddle point for Graph the…

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Q: 2 The equation of the tangent line to the graph y at the point (-1,2) is given by O a) y = 6x + 8. O…

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Q: . Find the average rate of change of y = x' over the interval [1, 3]. Determine the slope of the…

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Q: How many tangent lines to the curve y= x /(x+1) passthrough the point ( 1,2) ? At which points do…

A: Given : y=xx+1  pass through the point (1, 2) To find: The number of tangent lines to the curve  y =…

Q: find the slope of the curve y=x^2-4x-4 at the point P(3,-7) by finding the limiting value of the…

A: Now let the secant line passes through the points  Now slope of the secant line is,

Q: a moving point is equidistant from the point (a,0,0) and the line x+a=0,y=0.Find the value of z^2

A: Let us assume that the point is = x,y,z The distance between the point a,0,0 and point x,y,z is:…

Q: Calculate the length of the curve defined by Vy(y-3)on the interval 1 < y < 9. x =-

A: Solution: Consider the given curve: x = 13yy-3 on the interval 1≤y≤9 Since we know that the arc…

Q: If f(x,y, z) = x²y cos(2ryz), find the rate of change in the function at the point (x, y, z) = (1,1,…

A: The gradient of the function is defined as ∇f=⟨fx,fy,fz⟩. The directional derivative in the…

Q: 2. If you will draw the graph of y = x(x+2)², how will you sketch it with respect to the x-axis? A.…

A: Solution..

Q: 23. A tangent line drawn to the graph of y = 2x/(1+ x²) at the point (2,0.8) forms a right triangle…

A: Given: y=2x1+x2; 2,0.8 we know that for finding equation of tangent at point2,0.8, first we need to…

Q: Can you help me step by step?

A: Given equation of curve is y=ax2+bx+c which passes through (1, 3) so point (1, 3) will satisfy the…

Q: Find the slope of the curve x^3=(y-x^2)^2 at (1,2). If q-p=Inq+Inp, find dq/dp.

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Q: The tangent line to the graph of y = g(x) at the point (6, 4) passes through the point (2, 9). Find…

A: The tangent line to the graph y=g(x) at the point (6,4) passes through the point (2,9). Note:…

Q: A. Find the slope of the curve y = x² - 2x - 4 at the point (2, -4) by finding the limiting value of…

A: A. Find the slope of the curve y = x² - 2x - 4 at the point (2, -4) by finding the limiting value of…

Q: Find all points where the functions have any relative extrema. Identify any saddle points.ƒ(x, y)…

A: Given function is f(x,y)=x2+4y3-6xy-1.

Q: ve y = ax 2 + bx + c passes through the point (2, 4) and is tangent to the line y = x + 1 at (0, 1).…

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Q: IT Find the length of the curve y= in (cos x ), 0 < x < 4

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Q: Find distance between point A(1,3) Perpenclicular the line L: 2y =2+X on

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Q: find curves y = y ( x ) such that every point ( x 0 , y 0 ) on the curve divides the tangent line…

A: step:- 1 Section Formula:- Let SQ be a line segment with end points S (a1,b1) and Q (a2,b2) then let…

Q: 9. Find the width of the shape, surrounded by two curves y = e*, y = e¯ * and %3D two straight lines…

A: Consider the given curves y=ex and y=e-x and two straight linesx=ln2 and x=ln5.

Q: 13. BONUS: Find the coordinates of all points on the graph of y=1-x at which the tangent line passes…

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Q: The straight line y=x +B is tangent to the graph of f(x) = 2^{x at the point where x = A. Find A and…

A: The staright line y=13x+B is tangent to the graph of f(x)=2x at the point where x = A, we have to…

Q: ● If the pollution index of a point (x, y) is given by p(x, y) = x². Calculate the total pollution…

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Q: Find the points on the curve where the tangent is horizontal or vertical. x = t3 − 3t,    y = t2 −…

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Q: Two hours after the start of a 100-kilometer bicycle race, a cyclist passes the 74-kilometer mark…

A: Solution is done in step 2

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 for which y" = x passes through the point (1, –1) with a slope of. Find the y-value of at x…

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

Q: The curve y=ax² +bx+c_passes through the point (1,2). The line y=2x+1 is tangent to the curve when…

A: We have to solve

Q: 1. Find the orthogonal trajectories to the family of curves r+y = ce". Include the graph showing…

A: We are given an ordinary differential equation. We need to find its orthogonal trajectories which…