1) Let z = 2+i be a point on a curve C. The direction of the tangent vector to C at z = 2+i is rotated through an angle θ under the action of the transformation  f(z) =36z2+12z  on C. Then the value of tan θ is. 2) The image of the line y = 5x under the mapping w = z2 is a straight line L. Then the slope of L is 3)A non-zero fixed point of the mapping w = 14z/(11z+2) is 4) If u(x,y) = 2x+3xy+c is the real part of an analytic function f(z), then the derivative of f at 5i, f'(5i) =

Q: Find the points on the curve c where the tangent is vertical C: x= t - 48t, y = t + 12t. ОА (-128,…

A:

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: Sketch a contour map for the graph of the equation z = 2² + y². Include level curves corresponding…

A: In question we need to draw a contour map.

Q: 8. The rectangular function is defined by: A, (0) - {₁ T - sts Plot the following rectangular…

A: All the graphs are plotted below.Explanation:Here are the plots:

Q: Find the point-slope equation of the tangent line to the parametric curve given by x = 1+ 2t° and y…

A:

Q: the coordinates of the shadow point k (5,-4) which are translated by T=((-2)/(1)) and followed by…

A: The given point is:k=(5, -4)

Q: 4. Point C (-5, 4) is reflected over the X-axis. What are the coordinates of C'? O a) (5, 4) O b)…

A:

Q: Construct a linear map L(z)=az+b that will send the imaginary y-axis to the line v=-u.

A: we have to constract a linear map that maps the y-axis to the line v=-u Basically we have to…

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: 11. The point (9, 16- A. (3,4)

A: y=f(x)after transformation y=f(x)(x,y)→(x , y)(9,16)→(9 , 16)=(9,4)

Q: 4. Which graphs of ƒ may have a point of inflection? State the coordinates of each point a) ƒ''(-4)…

A: For a function f, if its second derivative f″(x) exists at x0 and x0 is an inflection point for f,…

Q: Considering the following graph of the given function f. y The xy-coordinate plane is given. The…

A:

Q: The equation below defines y implicitly as a function of x: 2x2 + xy = 3y2 Use the equation to…

A:

Q: Determine the equation of the tangent to the graph of y- x - 3x + x+3 at the point (- 1, -2). O a)…

A: We have to find the tangent of the given function at point (-1,-2).