Write the equation of a circle osculating with the curve f(x)=arctanx at the point x0=1.

Q: Find the equation of the tangent line to the curve x' + y' = 6xy at (3,3). Write the equation in…

A: Given the curve x3+y3=6xy We need to find equation of the tangent line to the given curve at (3,3)…

Q: Use the guidelines of this section to sketch the curve   y =  x - 3x 1/3

A: Let us make a table for the function x -8 -1 0 1 8 y -2 2 0 -2 2

Q: y= x² +9

A:

Q: Use the guidelines to sketch the curve  y = 2 x2  / ( x 2  -1 )

A: For, x=0, y=0  So, the y-intercept is 0   Then we plug y=0 and find x so, x-intercept is 0.

Q: What is the equation of the tangent line to the circle x2 + y? = 34 at the point (5, 3)?

A:

Q: What are the coordinates of the points in the graph of y? – x² + 6x – 13 = 0 in which the tangent…

A: y2-x2+6x-13=0 --------------(1) Differentiating with respect to x ddxy2-x2+6x-13=ddx(0)…

Q: Given circle x+y= 25, find the slopes of the tangents to the two points on the circle where x =-3.'…

A: Consider the given circle x2+y2=25. Obtain the slopes of the tangent to the two points in the circle…

Q: Does the curve y = x4 - 2x2 + 2 have any horizontal tangents? If so, where?

A: Consider the given function y=x4-2x2+2.

Q: Use the guidelines of this section to sketch the curve.   y = 2√ x    -x

A: We will make a table for the function  x 0 1 4 9 y 0 1 0 -3

Q: Find the point in the first quadrant on the curve y = x + x - l closest to the origin.

A:

Q: Find the equation of the tangent to the curve y= 3x' – 4x² +2x–10 at the points where the curve cuts…

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Q: Use the guidelines of this section to sketch the curve   y =x / ( x3  -1 )

A: Given: To sketch the given curve using the guidelines.

Q: Graph the parabola f(x) = x2 . Explain why the secant lines between the points (-a, f(-a)) and (a,…

A: We have the given equation of parabola as fx=x2 On considering the solution set, which satisfy the…

Q: Use the guidelines of this section to sketch the curve.   y = x/ x2-9

A:

Q: Write the equation of the tangent line to the graph of y = x2 at the point where x = 2.5.

A: To find the tangent line to a function at a given point first find the first derivative of the…

Q: Find the equation of the tangent to the curve r = θ when θ = π/2

A: Given problem:- Find the equation of the tangent to the curve r = θ when θ = π/2

Q: Find the slope and the equation of the tangent line to the curve y=x²+1 at x=0. Sketch the graph

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Q: Use the guidelines of this section to sketch the curve.   y = (4 - x2)5

A:

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

A:

Q: Use the guidelines of this section to sketch the curve   y =2 sqrt x - x

A: Given              y=2x-x

Q: Find an equation of the line which is tangent to the circle r +y - dr + by – 12 = 0 at the point (5,…

A:

Q: Hello, could you please help me determine the equation of the line tangent to the curve…

A: The given curve is: x2y+2xy2=x+6y

Q: Determine the equation of the line tangent to the graph given by y = at the point x +1 (4, }).

A: To find the equation of the line tangent to the graph y=xx+1 at the point 4,25

Q: What equation is tangent to the circle (x-4)² + (y- 2)* = 25 at the point (8,5)?

A: concepts remember for this question are; 1. The general equation of a straight line is y = mx + c,…

Q: Find the equation of the tangent line to the circle at the point (-3, -4). Equation of the circle *…

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Q: Use the guidelines of this section to sketch the curve.   y = 2 + 3x2 - x3

A:

Q: Use the guidelines of this section to sketch the curve. х — 6 y = x2

A:

Q: Use the guidelines of this section to sketch the curve.   y= 3√(x2  -1)

A: We need to find the x intercept, y intercept, vertical asymptotes, horizontal asymptote etc to…

Q: Find the equation for the line tangent to the curve 2exy = x + y

A:

Q: Use the guidelines of this section to sketch the curve.   y = 1/ x2 -9

A: Let us plot a table with values of x and y. x y 0 -8 1 -8 -1 -10 2 8.75

Q: Use the guidelines of this section to sketch the curve.   y = x √(5- x)

A: We can not have negative number inside square root So, 5-x≥0 x≤5  Let us make a table of values x…

Q: Use the guidelines of this section to sketch the curve.   y = x 5   - 5x

A: We make a table with different values of x and y.  x y  0 0 1 -4 -1 4

Q: What equation is tangent to the circle (x-4)^2 + (y-2)^2=25 at the point (8,5)?

A:

Q: Find the closest point to the point (2,0) on the y = x curve.

A: To find the closest point to the point (2,0) on curve y=x

Q: Find the equation of the tangent to the curve y=x²-x -2 at the point (1, -2).

A: We have to find the equation of the tangent to the curve y=x2-x-2 at the point (1,-2).

Q: Find the equation of the tangent and length of the tangent to the curve y= x2+1 at (1,2)

A:

Q: Try to find the slope of the tangent to the circle x²+y²=5. at the point (-2, 1) Show solution

A: tangent

Q: Sketch the curve y cu. = x sq.

A: Given the curve is y3 = x2 Put random value in the curve and we get the table which help to trace…

Q: solve for the equation in standard form then graph -Circle tangent to both axes at (−3,0) and…

A: solve for the equation in standard form then graph -Circle tangent to both axes at (−3,0) and…

Q: Find the points on the curve where the tangent is vertical. x=1³-3t, y-t³-31²

A: First we find dy/dx

Q: Find the standard form of the equation of the circle tangent to both axes at (-3,0) and (0,3).

A: Given that: The circle is tangent to both axes at (-3, 0) and (0, 3)

Q: Use the guidelines of this section to sketch the curve   y = x e -x

A: Consider the given function as y=xe-x

Q: Give the equation of a circle tangent to the line 3x + y -2 = 0 at (-1, 5) and with a radius equal…

A: Topic = Circle

Q: Find the equation of the tangent line to the graph of y = arcsin a when V2

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

Q: Find the point of inflection of the curve y= -x^3+x^2-x+1

A: The expression for the curve is given as, y=-x3+x2-x+1 The expression for the point of inflection…

Q: Find an equation of the tangent to the circle x 2 + y 2= 25 at the point  (3,4)

A: x2+y2=25 Differentiating with respect to x, we get 2x+2y·dydx=0⇒2y·dydx=-2x⇒dydx=-xy Now slope of…