The point P(1, ) lies on the curve y = x/(1 + x). (a) If Q is the point (x, x/(1 + x)), use your calculator to find the slope m of the secant line PQ (correct to six decimal places) for the following values of x: (i) 0.5 m = (ii) 0.9 m = (iii) 0.99 m = (iv) 0.999 m = (v) 1.5 m = (vi) 1.1 m = (vii) 1.01 m = (viii) 1.001 m = (b) Using the results of part (a), quess the value of the slope m of the tangent line to the curve at m = (c) Using the slope from part (b), find an equation of the tangent line to the curve at y =

Q: 3. Find the equation of the tangent line to the curve y = x2 – 3x + 4 that is perpendicular to the…

A: As per the company's guidelines,  we are supposed to solve first question for you,  kindly repost…

Q: Find an equation of the line tangent to the curve defined by z2 + 6ry +y = 32 at the point (2, 2).

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Q: -1 What is the slope of the line tangent to the graph of y at x = -2?

A: Find the derivative of y to obtain the tangent as shown below: y'=ddxtan-1xy'=1x2+1

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Q: 2. Find the slope of the tangent line to the curve y = 4x² – 2 at x= 1. What is the equation of the…

A: The given curve is y=4x2-2. At x=1, y=412-2=2. Thus, the graph is passing through 1, 2. The slope of…

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A: We will solve the problem

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Q: At which points on the curve y = 1 +°40x³ – 3x³ does the tangent line have the largest slope? | (x,…

A: Maximize slope

Q: Find the equation of the tangent line to the curve y²(y² – 4) = x² (x² – 5) at the point (0, –2). |

A: Equation of tangent line is given by:y-y1=dydxx=x1·(x-x1)      .............[1]So first find dydx at…

Q: 3. Find the slope m of the tangent lines to the parabola y = -x+ 5x+ 6t its point of intersection…

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Q: 3. Find the equation of the tangent line to the curve y = x2 - 3x + 4 that perpendicular to the line…

A: we have to find the equation of the tangent line to the curve y=x2-3x+4 that is perpendicular to the…

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Q: 7) Find an equation of the line tangent to the curve y = x+5 at x = 3. х-1

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Q: At what point on the curve x = 3t2 + 2, y = t3 – 2 does the tangent line have slope ? (х, у)

A: Slope of the line = dy/dx To get dy/dx, first get dx/dt then get dy/dt. Now divide dy/dt by dx/dt.5

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Q: 3) Find all points (x, y) on the graph of x2/3+y²/3 = 8 where the tangent lines have slope –1.

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Q: At what point on the curve x = 6t2 + 5, y = t3 − 1 does the tangent line have slope of 1/2?

A: We can use application of derivative in order to solve the given problem.

Q: (B): Find an equation for the tangent and normal Line to the curve (y 2x +4x-3) at (x1)

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A: Consider the curve

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A: To determine the x-intercept of the curve and slope of the tangent at the intercept.

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A: The solution are next step

Q: 9. Find the points on the graph y = х-2 7x - where the slope of the tangent line is parallel to 28х…

A: Given-  Consider the graph y=7xx-2. To Find- The points on the above graph , where the slope of the…

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A: Calculate the differentiation:-

Q: a) Find the slope of the tangent to the curve y = 3+ 4x2 – 2x³ at the point where x = a.

A: We are suppose to solve the problem by application of derivative.   NOTE :: As per our guidelines we…

Q: If y=mx+b is the equation of the tangent line the curve y=x2-3x+5 , which is parallel to the secant…

A: Proceed as shown

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Q: The slope of the tangent to the curve y²x + y²a² = 6 at (2, 1) is A B) -1 в 14

A: We can find the slope of the tangent to the curve at the indicated point as below.

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A: To find the x-intercept we plug y=0

Q: 9. Find the point on the graph of y = x² where the tangent line is parallel to the line 3x – 4y = 4.

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A: Given query is to find the slope of the tangent at given point.

Q: 2. Find the equation of the line that is tangent to the curve y 3 + 3y = x 2 at the point (2, 1).

A: Find the equation of the line that is tangent to the curve y3 + 3y = x2 at the point (2,1).