Problem 4: For what valnes of a and o s the line y=-2x+b tangent to the parabola y=Ox° whern X=2?

Q: Problem IX: Evaluate |-ds where C is the portion of the curve y= Vx from the point (1, 1) to the…

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Q: (x-4)2 (y+1)² Problem #4: Find the slope of the line tangent to the conic section 16 = 1 at (4,6)).…

A: We can find the slope to the conic section at the given point as below.

Q: Problem 3. Find the shortest distance between the point P (0, 1,0) and the line l given by x = 1-t,…

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Q: Question 12 y = Inz. Show that there is a line that is simultaneously tangent to both the curves y =…

A: In the question we have show the line which is tangent to both ex and lnx

Q: Problem 3.4 Find the points on the curve y = 2x3 + 3x2 – 12x +1 where the tangent is horizontal.

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Q: Problem 3.13 Find all points on the curve x²y? + xy = 2 where the slope of the tangent line is –1.

A: See the details solution in below

Q: Question 7 What is the equation of the tangent line to the curve y = In(x"+1) at x=17 A y=2x+In2 - 1…

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Q: Problem 3: Evaluate ff,F· dA using Gauss, where F = half of the sphere x2 + y? + z²2 = 9. (2²x, y³ +…

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Q: Ex(4) A particle moves from point (-2,5) to y-axis in such a way that Ay = 3Ax. Find its new…

A: Solution is given below:

Q: QUESTION 2 If e) - land f (0) - 6 then the equation of the line tangent to the curve y-for) at…

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Q: #10

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Q: Question 29 Determine an equation for the line tangent to y² = x³ = x + 1 at (1, 1). Oy=-x y = x ° y…

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Q: Problem 1 Evaluate the line integral / 2* ds, where C is the line segment from (3,0) to (0,4) in the…

A: Given line integral ∫Cx2ds, line segment (3,0) to (0,4)

Q: Question 15 Find the distance from S= (1,1,5) to the line L: x=1-t, y=2-1, z=31.

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Q: Problem 3.3 Find the equation of the tangent line and normal line to the curve at the given point.…

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Q: Question 7 What are the coordinates of the points in the graph of y2-x2+6x – 13=0 in which the…

A: Explained below

Q: Written Problem 3: An Acura and a BMW are driving around an empty planar parking lot, represented by…

A: ----------------------------------------------------------------------------------------------------…

Q: QUESTION 24 For the curve y = ax + bx + 12x - 7, what values of a and b will make the tangents to…

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Q: Find equations of (a) the tangent plane and (b) the normal line to the surface 2(x−2)2 + (y−1)2 +…

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Q: 56. Use the Greek method described in Problem 55 to find an equation of the tangent line to the…

A: Solution:Given x2+y2-4x+6y+4=0 at the point (3,22-3)To find the equation of the tangent

Q: Question 5 Two different level curves of the graph of z = f(x, y) can intersect. O True False

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Q: Problem 3 Find a curve in the xy-plane passing through the point (1, 3) and for which the normal…

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Q: Question 3 Let f(z) 2r-3z2-6z+2. Find the the equations of all tangent lines to f which are parallel…

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Q: Question 9 In the ry-plane, how many horizontal or vertical tangent lines does the curve æy? = 2 +…

A: Given a equation of the curve, xy2=2+xy To find horizontal or vertical lines of the given curve.

Q: Problem 6: Find the surface area of the surface generated by revolving the graph of f(x) = Vx from x…

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Q: can you please ans 2.8?

A: x = 3t2 + 1    ...................(1)y = t3 - 1     ...................(2)Points = ?  where slope=…

Q: Problem 2: Let F be the 3-dimensional figure whose base is the region bounded by the circle a? + y =…

A: Given the region bounded by the circle x2+y2=9. The height of the cross-section is 3-x and its…

Q: Question 3 Suppose C=0, so that 2y 24y 5x3 = 0. Find all points (x,y) at which the tangent line to…

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Q: Question 14 A line is tangent to y = x³ - 2 at (2,6). What is the coefficient of x when the line is…

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Q: Problem 4. Given a generic parabola y = ax, find the slope of the tangent at any point (x, y).

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Q: Problem 10. Find an equation of the line tangent to the curve defined by x + 6.xy + y* = 72 at the…

A: Differentiate the given equation and get slope of tangent at (2,2):…

Q: Problem 8. Find equations for the tangent plane and normal line at the point Po on the given…

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Q: Problem 2: Let C be the boundary of the triangle with vertices 0, 2+ i, and 3i. (a) Find the line…

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Q: QUESTION 15 Find the area bounded by the curve y = 16 4 square units 16 square units 10 square units…

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Q: Question 8: 3. Find the equation of the line normal to the curve defined by the equation xy - 5=x-…

A: (a) Consider the equation

Q: Problem 4: Find the vector function that represents the curve of intersection for the following…

A: Given surface 1 is, x2+z2=9 Given surface 2 is, x2+y2+4z2=25........(1)

Q: Problem 13. Determine the acceleration of a car moving on a curved path from point A (as the…

A: y=-1.5x2+3

Q: Question 10 Find the equations of the tangent plane and normal line to Xfy+7=4z at the poine (-3, 1,…

A: Given: Given: at the point (-3,1,-2)

Q: Problem 3. Find the curvature of the curve given (t). at the point ( LD

A:

Q: Problem IX: Evaluate -ds where C is the portion of the curve y= Vx from the point (1, 1) to the…

A: ∫xyds ds = dxi+dyj ds =dxi +12xdxj ds=(i+j2xdx ∫14xxi+J2xdx

Q: Problem 6 / (3y – xª + 2) dx + (5x + sin y*) dy, where C is the counterclockwise- Use Green's…

A: Given ∫C3y-x4+2dx+(5x+siny3)dy Where C is the counterclockwise oriented boundary of the triangle…

Q: Problem 4 A Calculate the equation of the tangent line to the curve 2x3 + xy +3x+ y = 2 at the point…

A: Given, Equation of the curve :    2x3 +xy +3x+y = 2   We have to write the equation of the tangent…

Q: Problem 6. Consider the curve defined by y2 – 4xy + 2x? = 7y. Write the equation of the tangent line…

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Q: Please show all steps to your solution and explain all work clearly. Midterm is based on Chapters P…

A: Given function is Differentiating both sides with respect to x , we get

Q: Example 19: (a) If x +y = 25, find dy/dx. (b) Find an equation of the tangent to the circle x +y =…

A: As asked we can find the necessary answers as below

Q: Question 1. Find f(4) and f'(4), assuming that the tangent line to y = f(x) at a = 4 has equation…

A: Giveny=10x+7

Q: Problem 2.8 At what points on the curve x = 3t2 + 1, y = t³ – 1 does the tangent line have slope .…

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Q: Problem 5. Find an equation of the tangent plane to the surface z = In(2x + y) at the point (-1,…

A: The equation of a tangent of the surface F(x,y,z)=0 at the point (x0,y0,z0) is given by,

Q: Question 9. A curve is given by y = v3x – In(3x). Find the minimum of the curve inside the interval…

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