If an inflection point of the aurve f(x)=acos(2.x) +bsin(3x) is P(z/6,5), then what are the real numbers a and b ? A) a = 0,b=1 B) a =-1,b=D1 C) a= 18, b=-4 D) a = 2,b=1 E) Does not exist

Q: Find the distance between the planes 5x − 3y + z = 2 and 5x − 3y + z = −3

A:

Q: The distance from (6,-5, 1) to yZ-plane is OA 6 /26 OC 1 O D. 62 OE 5 В.

A:

Q: Consider the right triangle withvertices (0, 0), (0, b), and (a, 0), where a > 0 and b > 0.…

A: Given right angle triangle has vertices  (0, 0), (0, b), and (a, 0), where a > 0 and b > 0.…

Q: (7) Let D be the solid above the cone z = r and below the sphere of radius 2, and let fla, 4, 7) =…

A: To convert the cartesian coordinates into cylindrical coordinates put  And the integral will be…

Q: Find an appropriate parametrization for the given piecewise-smooth curve in R'. The triangle formed…

A: Given that the triangle formed by travelling from the point (1,2,3) to (0,-2,7), to (6,4,2) and back…

Q: 5. (6 + 15i ) 3

A: this is a problem of complex analysis.

Q: A The roots of Characteristic equetion f oreler, lineor homopeneous-equation with constant…

A:

Q: Find the ar ea of sur face x - 2y - 2z = 0 that lies above the triangle bounded by the lines x = 2,…

A: Given :          The surface x2 - 2y - 2z = 0 that lies above the triangle bounded by the lines x…

Q: An angle with its vertex at the origin of an xy-coordinate plane and with initial side on the…

A: We know, An angle with its vertex at the origin of an x-y-coordinate plane and with initial side on…

Q: The tangent plane to the graph of the function f(x,y)=x+xy+y2, which is parallel to the z=1+2x+3y…

A:

Q: A B What other information is needed to prove AABCY ACDA by the HL Theorem?

A: Given : ∆ABC≅∆CDA

Q: A natural cubic spline is defined by Sa,(x-1)' +b,(x-1)² +c, (x - 1) + d, S(x) =- if 0sxs1 (x- 1)' +…

A: Step:-1 Since, we know for cubic spline S(x)=S0x=a0x3+b0x2+c0x3+d0…

Q: A funchion is defined by +the formua a f(x)=Ź ) which of the follauing is the %3D value of

A:

Q: 4) Use Green's Theorem to evaluate f √1+x³dx + 2xydy. C is the triangle with vertices (0,0), (1,0),…

A:

Q: 5. What is UF, where F = Ø? Prove the correctness of your %3D | computation. answer

A:

Q: 3) Use Green's Theorem to evaluate o-ydx+xydy where C is the line segment from (-2,0) to (2,0) then…

A:

Q: S how that the line af intesection of the Planes and 5x-2y-Z=0 X+2y-22= 5 is Paralkel to thelime メ+3…

A:

Q: When is An angle in the xy-plane is said to be in standard position?

A: An angle is in standard position if its vertex is located at the origin and one ray is on the…

Q: b) By using De Moivre theorem, calculate in the form of a + bi: 4. i) (VZ – iv2)* | ii) (1– i)6

A: Given (2-i2)4 &   (1-i)6

Q: Q) show that the pánts ACI,1,4), B(2,2,2), C (o,1,5) and D(1,0,5) ave coplanear (in the Same plane).

A: The given points are: A=1,1,4B=2,2,2C=0,1,5D=1,0,5 To prove: A, B, C and D are coplanar (they lie in…

Q: Compute f, f for f(z) = sin(5z) and path y that is the line segment from 3 – 6i to -6+ 6i.

A:

Q: find fvelume of Solid f in the octant that is below porabalord そこ16-メ-9 planes X:0,9:0I and Z=0. and…

A:

Q: function holomorphic in 2 except p in an open neighborhood of w, the

A: To prove, ∫Tf(z)dz=0

Q: 1. A such that the difference in distances between (x, y) and two fixed points (called is the set of…

A: A___ is the set of points (x, y) in a plane such that the difference in distances between (x, y) and…

Q: 2. (– 13 + 3i)31

A:

Q: If y = xsinx then prove that y''+y=2cosx

A:

Q: Determine una ecuación del plano tangente a la superficie dada en el punto especificado *:(-4, 2,…

A:

Q: Which of the following is the least distance from the point (2, –1,1) to the plane x + y – z = 2?

A: Given: The plane equation is x+y-z=2and the distance from the point is 2,-1,1 To find the least…

Q: z = tan (VZn + Ze

A:

Q: Prove that z'e'-z = 1 has exactly two roots inside the circle |z] = 1.

A:

Q: Find the Largest open rectangle in the plane in which the hypotheses of Existence and uniqueness…

A: Answer

Q: 1 4. Let f(=) =- s · Show that J (z)dz = 0 , where C is a simple closed contour not passing…

A: Moreras theorem

Q: 22 Find the Directional Derivabive of Pary,z)= xg-y2'+Z at the point CI, -2, 0) in the direcbion of…

A:

Q: Prove that dr-V3Ta? where こis the intersection of the plates: x²+ and and F=ly,Z,x)

A:

Q: 3. Find the orthogonal trayectories to the cuve y = ax²- acx Is held fixed. 3 .2 %3D where a

A: The curves that cut every member of a given family of curves at right angles, is called an…

Q: Show that fi(r) = rª and f2(r) = r² +1 are orthogonal on the interval [–1, 1).

A:

Q: Find the area of on of the triangle that can drawn between the planes 3x – 6y – 2z = 15 - and 2r + y…

A: For any triangle that will lie between two planes, one point has to lie on a plane and the other two…

Q: show that the. following Complex functron is dis continuous at z=i. fCZ) = スー! %3D 3.

A:

Q: An _____ is a set of points (x, y) in a plane such that the sum of the distances between (x, y) and…

A: The sum of the distances to any point on the ellipse (x,y) from the two foci (c,0) and (-c,0) is a…

Q: Find the area of on of the triangle that can drawn between the planes Зх — бу- 2г 15 and 2x + y - 2z…

A:

Q: to evaluate the line 12) Use Gren's Theorem integead along the posticy orientrch curre Jxy²dx…

A:

Q: Find the area of on of the triangle that can drawn between the planes 3x – 6y – 2z = 15 and 2r + y -…

A: The equations of the two planes are: 3x-6y-2z=152x+y-2z=5 As, 5,0,0 satisfies the equation of plane…

Q: In the standard (x,y) plane, what is the distance between (3, 4) and (6, 2)?

A:

Q: A flat, very thin table has a circular hole with radius 1 and a circular hole with radius 2. The…

A:

Q: 3 tari' (xty) , Prane that x2+ ydz Sen 2z be

A: We have z=tan-1x+yx-y This implies tanz=x+yx-y Let u=tanz Then we first need to find the degree of…

Q: Explain the fundamental theorem of albenra?

A: To explain: Fundamental theorem of Algebra

Q: Find the distance between the planes  5x − 3y + z = 5  and  5x − 3y + z = −9.

A: Two planes  and will always be parallel if The given planes  and  are parallel because we can see…

Q: Show that the sphere of radius 5, X(u, v) = (u, v, v25 – u? – v²) is regular.

A:

Q: Consider AGRT and AARE in the figure to the right. Given: R is the midpoint of AG and ET. Prove:…

A: Given: A figure with two triangles EAR and GTR. As R is the midpoint of AG, therefore, GR=AR As,…

Q: Let S be the portion of the cylinder y = 1 − x2 with x≥0; y≥0, bounded by the planes z = 2, and z =…

A:

Domain

In simple mathematics terms, a domain is defined as the space on which all the possible inputs for the function will lie. It can also be expressed as a set of departures for the required function.