b. Determine an equation of the line tangent to the curve at the given point. 2•y=38xy: (19,19) a. Verify that the point is on the given curve. Evaluate x +y for x 19 and y = 19.

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A: Given

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A:

Q: verify that the given point is on the curve and findthe lines that are (a) tangent and (b) normal to…

A: We plug x=√3 and y=2 in the given equation So the point is on the curve

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A: Given query is to find the equation of the tangent.

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A: Explained below

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A: The given equation is 4x3+3y2=52. Evaluate dydx using implicit differentiation as follows.…

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A:

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A: solution is given below

Q: (d) the equation of the line tangent to the curve at the point where (i) t =, and (ii) t = . = 17

A: We have x = 4sint,  and y = cost

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A: We find dy/dx using the implicit differentiation and we plug x=2 and y=1

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A:

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A: given  y=ax3+bx2+12x-7a=?b=?

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A:

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A:

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A: Substitute the point (-3,-1) in the given equation.

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A:

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A: Given: xy+2x-5y=2; 3,2 for finding equation of tangent, we need to find slopem1 of tangent  we know…

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A:

Q: 19. For what values of the constants a and b is (1, 3) a point of inflection of the curve y = ax³ +…

A: Consider the value of y and solve:

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A: Explanation of the answer is as follows

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A: Solution:- The given curve is  x+xy=6  ......(1) and point (4,1) we have to find equation of the…

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Q: Find an equation for the line tangent to the curve at the point defined by the given value of t. 10)…

A: Proceed as shown below

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A: use property of chain rule to find the slope and equation of tangent line

Q: 11. Find the slopes of the curve y y?- r2 at the two points shown hcrc. 2 (V3 = y2 - x?

A: we have the curvey4=y2-x2

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A:

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A: y=2x3-3x2-12x+20

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A:

Q: At the given point, find the slope of the curve, the line that is tangent to the curve, or the line…

A: Given y6+x3=y2+12x To find the slope of the curve , take derivative Given point is (0,1)