Q4: State the Fundamental Theorem of Independent of Path and Morera's Theorem. Why can't apply these theorems to compute the integral zdz, where C is closed contour.

Q: Find div F and curl F if F(x, y, z) = x³i - 10j+yzk. div F= curl F=

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Q: Let C be the upper half of the circle of radius 3 centered at (0, 0). Let f (x, y) be the square of…

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Q: Q2) homeomorphism. Prove or disprove: The function f: (R, T1) - (R, 13) defined by f(x) = 3x is a…

A: Clearly the given function f(x)=3x is continuous. Now we want to check whether it is bijective,

Q: Q5) A) Graph the curve Y= - 2x (x -4)(x + 6)(x - 2) between the value of x (0, 41. then find the…

A: y=2x(x-4)(x+6)(x-2)

Q: 1) Find the limited Zone of curves piven! area the remaining bet ween the 2. y = 9= x² and

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Q: Find div F and curl F if F(x, y, z)=xi - 10j+yzk. div F= curl F=

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Q: Q2) A) Graph the curve Y = x (x +5)(x-3) between the value of x [-5, 3], then find the area of the…

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Q: Find the Values of Constunts a, boc that maximum Value of divectional direchive. of T= any+Lyg+cg,at…

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Q: Find two positive numbers whose product is a such that their sum is minimum.

A: Let the two numbers are x and y So, xy=a y=a/x   Their sum= S= x+y We have to minimize S

Q: (z)dz

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Q: Verify Stoke's Theorem for F =( x²)i +(xz)j + (xyz)k and C is the curve of intersection between z=1…

A: Given: F =( x²)i +(xz)j + (xyz)k and C is the curve of intersection between z=1 and z² = x² + y².

Q: Find an analytic function whose real part is e-x (xsiny+ycosy)

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Q: 2.Proof that any tangent plane for the surface F(- point = 0 passses through a fixed

A: Given below clear explanation

Q: 2y + 1 f(x, y) = 1² X consider h as a continuous function of 1 variable, such that the value of h…

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Q: (a) Let f(2) = 24 +5z3 Evaluate the integral f(2)dz, where the contour C is the circle k| = 2.

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Q: rve Y= x (x+5)(x-3) between the va rea of the finite region bounded by ven quantity in terms of sin…

A: We have to find the following given conditions according to the given information

Q: Find div F and curl F if F(x, y, z) = xªi – 6j + yzk. div F= curl F=

A: To find  and  if .

Q: Evaluate the line integral 3xy ds where Cis line Segment Joining (-5,7) to (3,1) the

A: Introduction: A line integral in calculus is an integral where the function being integrated is…