The curve x^3 − y^3 = 1 is asymptotic to the line y = x. Find the point(s) on the curve x^3 − y^3 = 1 farthest from the line y = x.

Q: The slope of the tangent line to the curve y=4/x at the point (9,49) is:

A: To Determine: Slope of the tangent line to the curve at the point (9 , 49). Given curve is:…

Q: Calculate the length of the tangent line, normal line, sub-tangent and subnormal from: a. xy² = 18…

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Q: 3 Find the slope of the tangent line to x/y +yVx = 10 at (1,8).

A: given: x3y + y3x= 10differentiate given equation with respect to xx3 ddxy + y ddx x3+ y3ddxx+ x ddx…

Q: 4. Find the point(s) on the curve of y=,x+x+2for which the slope of the tangent line is zero. (5)

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Q: the tangent line  to the graph of y=lnx\x is perpendicular to the line x=7 at the point where?

A: The line x = 7 is perpendicular to x axis. Hence, it's slope is infinity. The tangent line that is…

Q: Find the slope of the tangent line to the graph at the given point.

A: Slope of the tangent line is the derivative of the given function at the given point. So…

Q: 8. Determine the equation of the tangent line to the graph of the lemniscate: 2(x2 + y2)2 = 25(x² –…

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Q: 4 The slope of the tangent line to the curve y = X at the point 5, is: 5

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Q: What is the value of the slope of the tangent line to the curve *y+y<=5 passing through the point…

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Q: The slope of the tangent line to the curve y 2x at the point 2, 16) is:

A: As we know that; The slope of the tangent line to the curve is equal to the derivative of the…

Q: Of the infinitely many lines that are tangent to the curve y= -Sinxand pass through the origin,…

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Q: 9. Find all the x-values on the curve where the tangent line is horizontal Y = 2x°(x- 3)°

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Q: Find the slope of the tangent line at the indicated point for: y = 2 at the point (1,2).

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Q: Show that the tangent lines to the graph of y = (ex - e-x) / (ex + e-x) atx = 1 and x = -1 are…

A: Here we have to show that the tangent lines to the graph of y=ex-e-xex+e-x at  x=1 and x=-1 are…

Q: What is the slope of the tangent line to the curve y = 2sin 4x at x = 4

A: Given, The curve  y = 2sin4x   We have to find the slope of the tangent line to the curve at x = π4.…

Q: There is a line through the origin that divides the region bounded by the parabola y = 4x – the…

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Q: Compute Δy Δxfor the interval [4,10], where y= 2x-6   ________   What is the slope of the tangent…

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Q: What is the slope of the tangent line to the graph of x^2-4y^2 + 2x + 4y = 8 at (4, -2)?

A: According to our guidelines In case of multiple questions we are supposed to answer the first…

Q: Find the slope of the tangent line drawn to the graph of −4x^2−xy+3y^3=−200 at the point (−1,−4).…

A: Given function is : -4x2-xy+3y3=-200 To find out slope of tangent dydx at -1,-4 Differentiating…

Q: There is a line through the origin that divides the region bounded by the parabola y = 4x – axis…

A: Solution

Q: Estimate the slope of the tangent to the curve y 0.25x at x = 2 algebraically by finding the slope…

A: We have to find the slope of the tangent to the curve at x=2 by finding the slope of the secant…

Q: 2. Find the slope of the tangent 2 line to the curve f (x) = - = -1 at x

A: topic - slope of tangent line to curve

Q: The slope of the tangent line to the curve y 4 at the point (4, 1) is: - The equation of this…

A: The slope of tangent to any curve is determined by the derivative . So, slope of the tangent…

Q: There are two lines passing through the point (5,-1) that are tangent to the parabola y = -x^2+4x.…

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Q: Ax) = (5x* - 3x)(2x° – 7x) en x =

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Q: There is a line through the origin that divides the region bounded by the parabola y = 3x – 4x² and…

A: we have been given the parabola y=3x-4x2 to find the points put 3x-4x2=0⇒x(3-4x)=0⇒x=0, 34…

Q: What is the value of the slope of the tangent line to the curve *y+y²=5 passing through the point…

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Q: is the tangent line to y= 1/2arctan(1/5x) at the point (5,π/8)?

A: Answer and explanation is given below

Q: There is a line through the origin that divides the region bounded by the parabola y = 4x - 5x² and…

A: Given that equation of parabola y=4x-5x2let ,equation of line y=mx   where slope=m which is devide…

Q: Find the slope of the tangent line to the parabola y= 2 +x−x^2 at the point (0,2).

A: Simply take the derivative of the given equation and substitute the given point.

Q: There is a line through the origin that divides the region bounded by the parabola y = 5x – 7x² and…

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Q: There is a line through the origin that divides the region bounded by the parabola y = 2x – 3x2 and…

A: According to company rule, we can answer only first question and rest can be reposted.

Q: Show that the curve y = 6x + 6x - 3 has no tangent line with slope 2.

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Q: Find an equation of the tangent line to the curve y = 2x2 + 3 that is parallel to the line 8x – y+ 3…

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Q: At what point on the curve  y = 4 + 2ex − 4x is the tangent line parallel to the line  4x − y = 9?…

A: Given, y=4+2ex-4x First, find the slope of tangent line parallel to the line 4x-y=9 Find the point…

Q: The slope of the tangent line to a curve at any point is (5x² - y) ex+y If the curve passes thru…

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Q: Find the slope of tangent line for the equation x^2+y^2=5 on (1,2)

A: The given equation of the line is,

Q: At what exact point on the curve y = 9 + 2ex 5x is the tangent line parallel to the line 5x – y = 4?…

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Q: There is a line through the origin that divides the region bounded by the parabola y = 7x – 2x and…

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Q: What is the value of the slope of the tangent line to the curve x²+ 4.xy +y² =13 passing through the…

A: topic - slope of a tangent at a point on a curve

Q: There is a line through the origin that divides the region bounded by the parabola y = 2x – 8x and…

A: There is a line through the origin that divides the region bounded by the parabola y=2x-8x2 and the…

Q: There is a line through the origin that divides the region bounded by the parabola y=7x-(2(x)^2) and…

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Q: 5- Find the slope of the curve and the tangent line of y = 2x- 3 at (0, 2).

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Q: Show that the curve y = 6 x 3 + 5x -3            has no tangent line with slope 4.

A: y=6x3+5x-3 has no tangent line with slope 4

Q: 2. What is the slope of the line tangent to the curve 8x3-y²=4 at the point (1,-2)? CAL normal line…

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Q: Calculate the length of the tangent line, normal line, sub-tangent and subnormal from: a. x²+ y²-4x…

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Q: Kappa Curve: x²y² + y* = 2x² %3D

A: We are asked to find the slope of the tangent line at the given point

Q: 2. Find the curve that passes through the point (1, 3) and whose tangent line at (x, y) has slope

A: Solve for the curve

Q: 13) Estimate tan(44°) using linear approximation.

A: