1. Compute each contour integral. The curve C is a given in the figure below: (a) fz²dz (b) foxdz (c) f(2z - 1)dz 1+i 4 1

Q: Find the abscissa of the point on the graph of y=V 2x – 1 that is parallel to the line 2x - y+1=0

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Q: Evaluate F. dr along the line segment C from P to Q. F = -8xi+y j; P(-2,0), Q(7,0) F• dr =

A:

Q: Find all values of the constants C and b such that the curve: y = C bx passes through the points…

A: Given Where C  and b are the constants It passes through the points (2, 76) and (3, 304)

Q: 2 Find the distance from the point B = [0 5 0 to the line 1 +t| 0 -3

A: Here we will find the distance between the given point and line,

Q: Find all points (x,y) on the graph of y = х- 2 with tangent lines perpendicular to the line y = 2x -…

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Q: Evaluate Pw.-(x+2y))- dr, where C is the curve shown below.

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Q: Find all intersections of the curve y = 10 - x and y = x + 8.

A: To find intersection point of the curves.

Q: Consider the point (x,y) lying on the graph of the line 8x + 7y = 3. Let L be the distance from the…

A: We use the distance formula

Q: Sketch a contour map and graph of . a. g(x, y) = 9x² + 4y² b. z = y/x

A: The given function is: g(x, y) = 9x2 + 4y2 The contour map of the above function is:

Q: Evaluate f (5ydy + 3xydx) C if C is the closed curve determined by the x-axis, the parabola y = x²…

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Q: a- Find the limits of the functions below: 7x3 - limx→0 3-3x²-6x x+2 limx--2 Vx²+5-3

A: “Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: c. Evaluate f 3x ds, where C consists of arc C₁ of parabola y = x² from (0,0) to (2,4), followed by…

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Q: Transform the function y=6x-1rlght 3, down 4 , and reflected over the x-axis

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Q: 3) Find the function of y = 1) Reflect about the (2) Shift up (3) Shift X-axis 8 Units left 7units

A: The given function is y=x1) Reflect about x-axis2) shift up 8 units3) shift left 7 units

Q: Trace the following curve:

A: Given curve: y=x4-6x2-7 Formulas used: ddxxn=nxn-1ddxconstant=0

Q: Evaluate + 5x)dx + (ye* – 3y²)dy where C is the boundary of the curve given below. -2

A: Detailed explanation mentioned below

Q: Find the value of c such that the line y = C = x + 3 is tangent to the curve y = c√x.

A: To find the value of  such that the line  is tangent to the curve .

Q: The line 2x + 5y = 1 meets the curve x² + 5xy - 4y² + 10 = 0 at the points A and B. Find the…

A: The midpoint of the line joining the points: x1, y1 and x2, y2 is x1+x22, y1+y22. The roots of the…