Show that the square of the length of subtangent at any point on the curve by 2 = (x+a)3,(b is not equals 0) varies with the length of the subnormal at that point

Q: Area of a regim enilosed is by Curves y= 12 and

A: To find the area enclosed by the given two equations

Q: Find the length of the curve x = 49 sec* t – 1 dt with 3 - - 6. Length is

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Q: Prove that the point of the tangent intercepted between the axes at any point on the curve xmyn=am+n…

A: Prove that , The point of the tangent intercepted between the axes at any point on the curve…

Q: Find the points on the curve  y = 2x3 + 3x2 − 12x + 3  where the tangent line is horizontal.

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Q: Find the x Coordinate of the point on the graph of 4=x² where the to the Secant. Longent tine.…

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Q: Find the length of the curve y x² Inx 8 at (2 <x< 4)? -

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Q: Find the points on the curve y = x3 + 3x2 - 9x + 8 where the tangent is horizontal. smaller x-value…

A: Explanation of the answer is as follows

Q: Find the points on the curve y = 2x3 + 3x2 12x + 2 where the tangent line is horizontal. (х, у) %3D…

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Q: Find the slope of the tangent in the positive x-direction to the surface z = 3x - 6xy at the point…

A: We have to find the partial derivative with respect to x

Q: What is the maximum vertical distance between the line y = x + 51 and the parabola y= x² over the…

A: Given: The line y=x+51 and the parabola y=x2 To find: Maximum vertical distance between given line…

Q: What is the area of the triangle bounded by the x and y axes and the tangent to the curve xy^2=4 at…

A: xy2=4 Differentiating with respect to x, we get…

Q: 2) Find and sketch the circle of cur vature at the point on the curve y = x2 where the tangent line…

A: To find and sketch the circle of curvature at a point on the curve y=x2 , where the tangent line has…

Q: Find the slope of the tangent line to the curve - 3x + lay+ 3y = 199 | %3D | at the point (1, – 4).

A: We are given a curve and we need to find out the slope to the tangent line at the point (1,-4). For…

Q: 13. Show that the length of the portion of any tangent line to the ball x2/3 + y2/3 cut off by the…

A: Given: The equation of the ball is: x23+y23=a23...........(1) We have to show that the length of the…

Q: Set up the itegral that represents the length of the curve for 4=L x4 +L 4x2 for 12x< 2. Do Not…

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Q: Find the points on the lemniscate where the tangent is horizontal. 8(x2 + y2)2 = 81(x2 − y2)

A: The equation for the lemniscate

Q: Find an equation of the tangent plane to the surface 9x2 + y2 + 4z2 = 25, at the given point (0, −3,…

A: Concept: The two expressions connected by equal to be called an equation. The expression on the two…

Q: is the equation af tangent line at X=/ y = mx+b. to the giaph of f c) =x² -x at x=/ m%= b.

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Q: Find the length of the curve y=lnx from x=1.5 to x=3.

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Q: Prove that the point of the tangent intercepted between the axes at any point on the curve x…

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Q: Find the length of the curve defined by y = 3z3/2 - 3 from x = 3 to a = 9. The length is

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Q: A curve passing through (1, 0) is such that the ratio of the square of the intercept cut by any…

A: We have to find the possible curves that satisfies the given condition.

Q: Find the points on the curve y = 2x' + 3x² – 12x + 1 where the tangent is horizontal. -

A: As per the instruction, we will be answering the first question. For (51), Given: y=2x3+3x2-12x+1.…

Q: show that the sum of the x-intercept and y intercept of any tangent line to the curve x1/2+…

A: Consider the given equation of curve, x+y=cddxx+y=ddxc12x+12ydydx=012ydydx=-12xdydx=-yx Therefore,…

Q: Find the slope of the tangent line to the circle x2+y2 = 4 at (1,-v3)

A: To find the slope of tangent line to the circle x2+y2=4 first find the derivative dydx.…

Q: y = -V16 – x², — х2, -4 < x < 0.

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Q: find the tangents as direccted to the curve y = x4 – 4x3 + 2x2 – 4x + 15, perpendicular to the line…

A: Given that  y=x^4-4x^3+2x^2+4x+15  Line is x+8y=7

Q: Show that the sum of the x - and y  -intercepts of any  tangent line to the curve  sqrt x + sqrt y =…

A: We find the dy/dx then we find the slope at a point (h,k) by plugging x=h and y=k

Q: Why is the limit of the secant line PQ to a curve as it approaches zero is the same as the slope of…

A: As h approaches zero, the slope of the secant line ms approaches the slope of the tangent line mt

Q: gion shaded in light blue is bounded by two curves, y = (x – 1)? + 33 (in dark red) and z+ 3)² + 1…

A: We will find the area between the curves.

Q: Find the points on the curve y = x + 3x2 9x + 1 where the tangent is horizontal. %3D smaller x-value…

A: The given function is y=x3+3x2-9x+1

Q: Find the are length of the curve 2x = 3 y over the interval from y=0 to y=1

A: To find: The arc length of the curve in the interval . Formula used: The arc length of the curve…

Q: Find the points on the curve y = 2x3 + 3x2 – 12x + 3 where the tangent line is horizontal. (x, v) =…

A: Solve the following

Q: a, given that the line ax+y+1 = 0 is tangent to the grapl

A: We have to find the value of a according to the given information

Q: Find the points on the lemniscate where the tangent is horizontal. 8(x2 + y2)2 = 81(x2 – y2) x, y)…

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Q: Find a curve in the xy-plane that passes through the origin and for which the tangent at (x, y) has…

A: Tangent is the line that just touches the curve at a single point. Derivative of the curve at a…

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

A: x=13yy-3,   1≤y≤9 Differentiating with respect to y, we get…

Q: Show that the slope of the secant line for f(x) = x 3 - 2x over[5,x] is equal to x 2 + 5x + 23. Use…

A: Given: y=fx=x3-2x; 5,x we know that slopem of secant for any given functionfx over a,b is given by…

Q: Find the points on the curve y = 2x3 + 3x2 – 12x + 1 where the tangent line is horizontal. (х, у)…

A: Solution ) given f(x) = y = 2x3 + 3x2 - 12x + 1 f'(x) = 2 × 3 × x3 - 1 + 3 × 2 × x2 - 1 - 12 + 0…

Q: on of the tangent to y = 3e" + 3ex that is parallel to

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Q: Find the minimum distance from the curvey y = 2x^2 to the point (4,0), correct to 2 decimal places.…

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Q: Find the set on which the curve is concave upward. Answer (in interval notation): 2 y = ₁² R² + ² +…

A: See the details solution in below

Q: Find the points on the curve  y = 2x3 + 3x2 − 12x + 6  where the tangent line is horizontal.

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Q: Find the points on the curve  y = 2x3 + 3x2 − 12x + 2 where the tangent line is horizontal

A: To obtain the points where the tangent line is going to be horizontal to the curve, we need to find…

Q: What is the maximum vertical distance between the y=x+2 and the parabola y=x^2 for -1 is less than…

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Q: find the points on the curve where the tangent is horizantal, X=t^2+1,y=3t^2+t

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Q: What is the average distance between the parabola y = 7x(16-x) and the x-axis on the interval…

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Q: Consider the curve satisfying y" = 6x and is tangent to the line y = 5– 3x at x = 1. What is y' (2)?…

A: Given: y''=6xand tangent to the line y=5-3x at x=1To find y'(2)=?

Q: Find the points on the curve y = 2x3 + 3x2 − 12x + 9 where the tangent line is horizontal. a)…

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Q: What is the maximum vertical distance between the line y = x + 38 and the parabola y = interval [–…

A: Given line equation is y=x+38 Given parabola equation is y=x2 From the above two equations x2-x-38=0…