(4) (а) Find a curve C such that C avoids both z = 1 and z = –32 and which is a branch cut for 23. Sketch the curve C (a rough sketch will suffice). (b) Let f(2) be the branch of z3 on C\ C such that f(1) f'(-32). e. Compute f(-32) and

Q: the line (x/a)+(y/b)=1 moves in such a way that (1/a\power{2})+(1/b\power{2})=(1/c\power{2}) ,where…

A: Variable line is                xa+yb=1                 ......(1)Any line perpendicular to (i) and…

Q: If y is a differentiate function of x, then the slope of the curve of; xy^2-2y+4y^3=6 At what…

A: given that y is a differentiate function of x then we have to find the slope of the given curve at…

Q: (x)=3x-2√x I the equation of the secant line through the points (4,f(4)) and (9, f(9)). w that there…

A:

Q: For the function f(x)=simplify the difference quotient: b) [(x+h)-700 What is the slope of the…

A:

Q: The level curves of the function f (x, y) = /2x² + y² – 1 are

A: Explanation of the answer is as follows

Q: Q3) Determine slope of a curve y = x + 2 at p(1,3) and q(3,11)

A: Slope of a curve : The slope of a curve y=f(x) at a point P is the slope of the tangent at that…

Q: What is the slope of the secant line that passes through the points(a, f(a)) and (b, f(b)) on the…

A: Given: The secant line passes through the points a,fa  and  b,fb. Concept used: The slope of a line…

Q: What does it mean for two families of curves to be mutually orthogonal?

A: Two families of curve are said to be mutually orthogonal if they intersect at right angles. Angles…

Q: 2(x2+y2)2=25(x2-y2) Verify (algebraically) that the following points are on the curve: (3, 1)

A:

Q: If a half-turn centered at F(3,7) is applied to the point A(9,12), what are the coordinates of its…

A:

Q: Evaluate A = F. dr where F(x, y) = (6x – 2y)i+x²j for each of the following curves. a) C is the line…

A:

Q: 5. nts) Let F =, use Green's Theorem to evaluate F. dr where the curve C is C the curve shown in the…

A:

Q: -3. 3) to the curve given by f(x) =

A:

Q: Assume that a rocket is in space and is following the path y = – 6(x − 7)² + 3, from left to right…

A:

Q: 3. Let f(x) = 2x - x². (a) Find the secant line to the graph of f passing through the points (0,0)…

A: We can find equation of secant line and tangent line .

Q: Prove that there no line through the point (0,1) is tangent to the graph of y = x*.

A:

Q: Let 13 20 x 20+ y = 2 be the equation of a curve in the xy-plane. Find the equation y = T(x) of the…

A:

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: Consider an F-curve with d f = (2, 14). Determine F0.05.

A: The F-curve 0.05 area with degrees of freedom 2 and 14.

Q: Find the orthogonal trajectories of the family of curves y = kx'. = C (C) 3 y³ +x? = C (D) 3 y³ + 3…

A: Given y5=kx5 To find the orthogonal trajectory

Q: (5) Find the curve y = f(x) in the xy-plane that passes through the point (9, 4) and whose slope at…

A:

Q: Let C1 be the curve r(x)= (x − lnx )i + (x +lnx )j, 1<=x<=e, and let C2 be the curve of y=et,…

A:

Q: Parameterize the line from (-1, 5) to (2, 3) so that the line is at (-1, 5) at t = 0, and at (2, 3)…

A: I am going to solve the problem by using some simple trigonometry to get the required result of the…

Q: Suppose the slope of the curve y = f¯¹ (x) at the point (4,7) is . Find ƒ'(7). [B] 4 [A] 1 [C] 5 [D]…

A:

Q: Consider the following graph. Let u-(t) = u(t – 7) be the unit step function shifted 7 units to the…

A: