Let f lany) prove that' flany) di f feren tiable I5 not point lo,0) .

Q: use B-furCtion definitionof devietive to prove that if fis diffevetiable arto, then fis…

A: Differentiability implies continuity

Q: a. Show that Ø, R E T. (by definition of Topology)

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Q: Show that |qbu)|&x + 7元? the closed on interval [-元,T」 fo1 -π2 2くだ gluen that glven gux) for

A: Given g (x) = x +x² To find the maximum value of g(x). We can differentiate the function and equate…

Q: Theorem 8o4 ŏ In a parallileguam, oppesitiangles ale equal aie

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Q: 2. Cuven that 7, = -2 +ui, Z= -2i + 3 and E, - |-i. Gvaluate the followshng %3D 2 | 국 2

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Q: The projection of u onto v is given by projvu = ________.

A: The projection of u onto v is given by projvu = compvu.

Q: (2,3) is te i చాంబ! Under a ro dediona Identidy three distinct point that Cald be the center & of

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

A: Given : ∆ABC≅∆CDA

Q: Show that : sup {reQ:r<a} =a, for each a e R. %3D

A:

Q: if f is derivable in [a, b] and f' (a) not equal to f' (b), then for each number k lying between f'…

A:

Q: matoix Such that show that Let is Then detx = tt mxn

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Q: 4).ェ Pare subset, -f y such that CeD than fic) is not eD, then the Convers %3D そイue.

A: Solution As it's mention C=D and f^-1 same , so each and every element from  f inverse we get equal.…

Q: A hransfoomation is definad by Hhe axa matox A=-a b-a atb Ifois an odd imtreger, prove %3D ushere a…

A: Since you have asked multiple question, we will solve the first question for you. If youwant any…

Q: 2)Evaluate exdA ,Ris bounded by y = x² ,y = 1

A: By using Fubini's theorem we solve the given problem.

Q: Roboto : Prove: 6. Alternate Exterior Angles Theorem Given: pllq 21 22 14px Two-Column Proof n H lo…

A:

Q: Let T cofinite topology on R and Y={5,6,7} find Ty?

A: We have to construct subspace topology with respect to the cofinite topology

Q: Find all angles between 0 and 2T satisfying the condition -1 Cs x = Separate your answers with…

A:

Q: 5. If r = (r, (x, y, z) and ro = (xo, Yo, 20), describe precisely the set of all points (r, y, z)…

A: We plug the given values in the given equation and simplify

Q: Prove the adentities. tano+ coto 1+ secolcsc 4-Cote I-tane

A:

Q: 2. (– 13 + 3i)31

A:

Q: 3) Consider the topology ↑ {GCR: 0 ¢ G or G = R} on R. Is open = %3D interval (-1, 1) compact in (R,…

A:

Q: Let W = Lin and U= Lin 2 (a) Show that R' = W U. Explain.

A: Note:- As per our guidelines, we can answer the first part of this problem as all the parts are…

Q: Show that close ball Y in a metfic space (X,d) is a closed set also show that if (X,d) is complete…

A: Show that closed ball Y in a metric space (X,d) is a closed set also show that if (X,d) is complete…

Q: Write a two Column proof. Given: Parallelogram JKLM Prove: AJKM ALMK 21. K

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Q: Prove:- The defect of a triangle in (RG) is an area function.

A: In Euclidean Geometry, the area of a triangle is calculated by multiplying the length of any side…

Q: b)use Cauchy Schwarz inequality to show that if Let u = and v = inequality to show that a² + b?

A:

Q: Quadrilateral RSTU with diagonal US ZR and ZTUS are right Zs TS > UR Given: Prove: U

A: Apply Pythagoras theorem on △URS. UR2+RS2=US2 . . . . . . . (1) Apply Pythagoras theorem on △TUS.…

Q: Prove that • I %3D

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Q: Q: Prove that tim x"- a" %3D

A: we have to find the limit of the expression

Q: Let (R, d) be discrete metric space, then R is not separ able O True O False

A:

Q: ) Prove that sac"()/T sec

A:

Q: Verify that the conclusion of Clairaut's theorem is valid, that is, that uxy = uyx u = x4y3 - y3…

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Q: dual of c, is isometric to l'.

A:

Q: 3) Consider the topology 7 = {G CR: 0 ¢ G or G = R} on R. Is open T 3= interval (-1,1) compact in…

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Q: Complete the proof that RT || UW. W Statement Reason ZSVU E 2TSV ZQSR E ZTSV ZSVU = ZQSR 4 RT UW…

A: The given query is to find the correct reason for the statement.

Q: Verify that the conclusion of Clairaut's theorem is valid, that is, that uxy = uyx u = x4y3 - y4…

A:

Q: Write a two column proof. Given: Parallelogram JKLM Prove: AJKM= ALMK 21. K

A: We can prove the question as below.

Q: Consider ỹ,,y2, ÿ,ER³ and that y,+y,+y;=0. For Î=span{ ỹ,,y} and Y=span{ỹ2, y, show that Î=Ỹ.

A: Given  that  y→1, y→2, y→3∈ℝ5 and that                   y→1+ y→2+ y→3=0→. and           Y^=spany→1,…

Q: Let V, 3 V3 = Vz= -3 8. %3D 131 2- -5 does { Vi,UeiVa} span R3?

A: Given vectors, v1 = 06-2 , v2 = 0-38 and v3 = 4-1-5 These vectors will span ℝ3 if they are linearly…

Q: Prove that du Inlul + C where n= -1 u

A:

Q: Suppose u, VE Vand ||u|| < 1 and ||v|| < 1 . Prove it: V1- ||u||?/1- ||u||2 <1- (u, v)|

A: Suppose u, v∈V and u≤1 and v≤1 We have to prove that 1-u21-v2≤1-u,v Here, we have  u≤1 and v≤1 Also,…

Q: /show that fo-1x is-Contindals everywhere.

A:

Q: Consider the topology 7 = {GCR:0 ¢G or G = R} on R. Is open interval (-1, 1) compact in (R, T)?…

A:

Q: By using Cauchy Residle Theorem 到一2p 121=1

A: First we have to find residue at singular points.

Q: Determine las primeras derivadas parciales de la función en el punto (1,2) (u, v) = z*y - 3yA O(1,2)…

A: Find the first partial derivatives of the function at the point (1,2) f(x,y) = x2y-3y4

Q: Which part (Given or Prove) of the proof depends upon the a) hypothesis of theorem? b) conclusion of…

A: (a) Hypothesis of the theorem :             The hypothesis of the theorem is been used for the…

Q: 8. Given: ON bisects LJOH, LJ = LH Prove: JN = HN JNH

A: here, in given ∆OJN and ∆OHN ∠JON=∠HON                                      ∵ ON bisect ∠JOH∠J=∠H…

Q: Explain the fundamental theorem of albenra?

A: To explain: Fundamental theorem of Algebra

Q: The segment addition postulate can't be proven using a two column proof. O True O False

A:

Family of Curves

A family of curves is a group of curves that are each described by a parametrization in which one or more variables are parameters. In general, the parameters have more complexity on the assembly of the curve than an ordinary linear transformation. These families appear commonly in the solution of differential equations. When a constant of integration is added, it is normally modified algebraically until it no longer replicates a plain linear transformation. The order of a differential equation depends on how many uncertain variables appear in the corresponding curve. The order of the differential equation acquired is two if two unknown variables exist in an equation belonging to this family.

XZ Plane

In order to understand XZ plane, it's helpful to understand two-dimensional and three-dimensional spaces. To plot a point on a plane, two numbers are needed, and these two numbers in the plane can be represented as an ordered pair (a,b) where a and b are real numbers and a is the horizontal coordinate and b is the vertical coordinate. This type of plane is called two-dimensional and it contains two perpendicular axes, the horizontal axis, and the vertical axis.  

Euclidean Geometry

Geometry is the branch of mathematics that deals with flat surfaces like lines, angles, points, two-dimensional figures, etc. In Euclidean geometry, one studies the geometrical shapes that rely on different theorems and axioms. This (pure mathematics) geometry was introduced by the Greek mathematician Euclid, and that is why it is called Euclidean geometry. Euclid explained this in his book named 'elements'. Euclid's method in Euclidean geometry involves handling a small group of innately captivate axioms and incorporating many of these other propositions. The elements written by Euclid are the fundamentals for the study of geometry from a modern mathematical perspective. Elements comprise Euclidean theories, postulates, axioms, construction, and mathematical proofs of propositions.

Lines and Angles

In a two-dimensional plane, a line is simply a figure that joins two points. Usually, lines are used for presenting objects that are straight in shape and have minimal depth or width.