(b) Find the slope of the line tangent to the polar curve r = 1- 2 cos e at the point where e = -2. Show the computations that lead to your answer. B I x² X2 0/ 10000 Word Limit

Q: If (x, y) = (-3, –3), then find the corresponding values of r > 0 and 0 < 0 < 2n in radians.

A: Explanation of the answer is as follows

Q: ) Prove that 2+sinZA Cos A-SinA

A: To Prove: cos3A-sin3AcosA-sinA=2+sin2A2

Q: Sketch the graph of r = 1–2 cos 0. Find tangents at the pole, all vertical and horizontal tangents.

A: Consider the given equation of graph.

Q: add or subtract formulas 2sin(t/2 +2pi/3) in sines and cosine without phase

A: In this problem, we need to express the given expression in terms of sines and cosines without…

Q: Convert r = 6(sin(0) + cos(0)) to an equation in rectangular coordinates in terms of x and y.

A:

Q: Assume that a particle's position on the x-axis is given by the equation X = 5 cos t+ 2 sin t where…

A: Concept - substitute t=0 in given position of particle

Q: The value of cosh(3z+1)dz, where C is the line segment from z=1 C to z= 2i. O a. (-sinh(6i+1)+sinh…

A: We have to find the value of integral,  I = ∮Ccosh(3z+1)dz  ;  where C is the line segment from z=1…

Q: find the length of the part of the r=2(1+ cosa) curve that remaîns în the r =211+ Sind) curve %3D…

A: We have to find the length of the part of the r = 2(1+cos alpha) curve that remains in the r =…

Q: (b) Differentiate y cos-1 23

A: Differentiate the given y with respect to x.

Q: If z = 4 - 3i in cartesian coordinates then z = 5ei® where 0(in radians) is: a. tan-'(4/3) + pi b.…

A:

Q: A. Integrate the following. i) (2x³-3x² +5x-2) dx ii) (5 sin20+2 cos 40) de B. Determine the area of…

A: A.Integrate the following.i) integrate (2x ^ 3 - 3x ^ 2 + 5x - 2) dx ii) integrate (5sin 2theta +…

Q: Show that COS x dx a² – x² sin a 2а where a is some positive number.

A:

Q: Plot each complex number: 1. -3i 3 2. 1. -2 -1 5. -11 -2

A: In complex plane  z = x + iy    = (x,y)

Q: Sketch the complete graph of r= 4 sin 0+2. First build a table of values

A:

Q: Show that the equation sin(cos 2x)= V1-4x² is an identity. %3D

A:

Q: = cos(2 arcsin()) Dilm i 0 272 0 0 0 0 0

A:

Q: 3. Find the area of one of the sine curve.

A:

Q: Use the double-angle formula for cosine to compute cos(20) given cos( os(0) = where 0 <0<. 79 90

A: Given.

Q: Find the Cartesian equation of the image of the line x = 2 under the mappingz → sin(z). Sketch…

A:

Q: Question 5 of 11 (3x-2+tanx-4)dx= O A. -4+ OB. -3x-2+sec²x + C +tant-4 C. 6x-2+tanx-4 OD.…

A: Given;  The integration of derivative of (3x-2+tanx-4).

Q: Graph the epitrochoid with equations x  =11 =cos t - 4 cos(11t/2), y = 11 sin t - 4 sin(11t /2)

A:

Optimization

Optimization comes from the same root as "optimal". "Optimal" means the highest. When you do the optimization process, that is when you are "making it best" to maximize everything and to achieve optimal results, a set of parameters is the base for the selection of the best element for a given system.

Integration

Integration means to sum the things. In mathematics, it is the branch of Calculus which is used to find the area under the curve. The operation subtraction is the inverse of addition, division is the inverse of multiplication. In the same way, integration and differentiation are inverse operators. Differential equations give a relation between a function and its derivative.

Application of Integration

In mathematics, the process of integration is used to compute complex area related problems. With the application of integration, solving area related problems, whether they are a curve, or a curve between lines, can be done easily.

Volume

In mathematics, we describe the term volume as a quantity that can express the total space that an object occupies at any point in time. Usually, volumes can only be calculated for 3-dimensional objects. By 3-dimensional or 3D objects, we mean objects that have length, breadth, and height (or depth).

Area

Area refers to the amount of space a figure encloses and the number of square units that cover a shape. It is two-dimensional and is measured in square units.