3. Which of the following are the abscissas of the points of intersection of the graphs of y = x – 1 y = x2 – 2x – 1 [A] 2 and 3 [B] 0 and 3 [C] 0 and 2 [D] 1 and 3

Q: a Show that y = mx + b intersects y = |x + 1| if m > 1 or m < -1. b Given that -1 < m < 1, find the…

A: Given,y = mx + cFor m &gt; 1Take  m = 2 &gt; 1,

Q: [2.18] Derive an explicit form of the polar C* of the following cones: a. C= {(x),x2):0 x2 s2x1}. b.…

A: To find- Derive an explicit form of the polar C* of the following cones: C = x1, x2 : 0 ≤ x2 ≤ 2x1…

Q: Let P denote the path that travels along the graph of y = x2 from (0,0) to (1,1). Let f(x,y) = √1 +…

A: Let P denote the path that travels along with the graph of y=x2 from (0, 0) to (1, 1). Let f(x,…

Q: Express K#S^2#T#2P as a connected sum of projective planes or as a connected sum of tori.

A: To express the given connected sum (of surfaces) in the required form

Q: WfSTC of the following statements are true? I. y = -x³ + 3x is symmetric to the origin. II. If f(x)…

A: To define given statement s are true or not

Q: 10 6) Let g(x) =+ 3 %3D x2 Is g(x) E [3,4], Vx E [3,4]?, using fixed point theorems what can you…

A: First we show that g(3)&gt;4 ,so g(3) does not belongs to [3,4]So we can not say that g(x) is in…

Q: Let C be the curve y = 2.5 In (6.25 – x²), for – 1.2 < x < 1.6. A graph of y follows. 4.6 4.5 4.4…

A: Here, y=2.5 ln6.25-x2. So,         y'=2.5ln6.25-x2'           =16.25-x26.25-x2'    =2.5·16.25-x2-2x…

Q: and f, and evaluate each at the given point. A(x, Y) = arctan(), (6, -6) %3D fx(x, y) = %3D fy(x, y)…

A: fx, y=arctanyx6, -6To find fx and fy

Q: Let X=ℝ2 and define d,:ℝ2×ℝ2→ℝ d2((x1 ,y1),(x2,y)2)) = max{|x1 - x2|,|y1 - y2|}. Draw the…

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Q: F· dr, where F(x,y) = –lj, and C is the part of the graph of y = - x from (2,2) to (–2, C

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Q: 2) Determine the dimension of Null A and Col A for the marix 1 2 30 0] A =0 0 1 0 1 0 0 0 1 0

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Q: Find and plot the cubic spline S satisfying S(0) = 1, S(1) = 3, S(2) = 3, S(3) = 4, S(4) = 2 and…

A: %File Name: findSplineCoefficient.m %Define function function [ retCoeff ] =…

Q: (G) G)- The projection of onto the line through zero 1 is and а. (;) () " () b. C. d.

A: Let u→=11, and the line l through zero v→=00, and w→=1-1. Need to find the projection of u→ onto the…

Q: 4.-Evaluate ſr f (z) on the given path: f(2) = z – 2i r It is a closed path that encloses 2i

A: Solution:

Q: the following curves. 33. y= 2.x+ 3x² + 1 34. y = x -x - 6x 35. y= x³ - 3x? + 3x – 2 36. y = 100 +…

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Q: [2 Lo 2. and defined T: R² → R³,by T(X) = AX. Let A Find the images under T of u = |E|, and v =

A: Given a linear transformation T:R2→R3 by T(X)=AX where A= 2002

Q: . Consider the accompanying graphs of y = 2r + 3 and y = In x. Determine the a. minimum vertical…

A: Given, y=2x+3 and y=lnx. And, the graph is shown below: a. Let Ax,y=x1,2x1+3 and Bx,y=x1,lnx1 be…

Q: Exercise 1.2.16 Find the circle x²+y² +ax+by+c=0 passing through the following points. а. (-2, 1),…

A: a) The given equation of the circle x2+y2+ax+by+c=0 Since the points (-2, 1), (5, 0) and (4, 1)…

Q: Let p(x) = kx* + kx + kx + k,x + kg, x E R be a polynomium without a first degree term whose graph…

A: The given polynomial is: p(x)=k4x4+k3x3+k2x2+k1x+k0

Q: 28. The locus of the points z such that /z 3/ = 2 is A. x² + y = 4 C. x* + y - 6y + 5 = 0 D. x+ y-…

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

Q: Prove that the following curves have infinitely many rational points: y? = a3 – 3x? + 3x – 1, y? =…

A: The given curve is y2=x3-3x2+3x-1. Rewrite this as follows. y2=x3-3x2+3x-1y2=x-13y=x-13         or…

Q: The graph of f(x) is the solid bláck graph below. WhlCH dotted graph? rep 10 -10 9 -8 -7 -6 5 6 7 8…

A: For the graph f(x), f(0)=0 And for the dotted graph g(0)=4 Now, for the solid graph, f(4)=1.5  And,…

Q: 2 -5 Let y = -3 and u = -4 -1 3 Compute the distance d from y to the line through u and the origin.…

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Q: Prove that H(x, y) = (x, –y) provides a conjugacy between x' = (4 })x and Y'= (; 7). X and Y' = 1 -1…

A: Given: X' =11-11XY' =1-111Y To prove: H(x,y) = (x , -y) provides conjugacy between both of the above…

Q: graph the points z = x + iy that satisfy the given conditions. 5. |z + 1| = 1 6. |z + i |= |z - 1|

A: Hi there, at a time we can answer only one question at a time and the exact one was not specified.…

Q: б. (a) Sketch the level curves z = k for k = 0, 1, 2 if z = x2 – y?.

A: The level curves of a function f of two variables are the curves with equations f(x, y) = c, where c…

Q: 2) Determine the dimension of Null A and Col A for the marix [1 2 3 0 0 A =|0 0 1 0 1 0 0 0 1 0

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Q: Show that the function f(x, y, 2) = (x² + y² + 2e**)4 is strictly convex on R³.

A:

Q: 3 4 Let y = -7 and u = -6 -4 1 Compute the distance d from y to the line through u and the origin. d…

A: The projection of a vector on a plane is its orthogonal projection on that plane. In simple words,…

Q: Consider the data: 0 1 2 3 4 f(x) -4 -3 -2 5 12 a) Applying the Composite Trapezoidal Rule with all…

A:

Q: 5. Identify and sketch the graph of the following equations in R³. (a) a2 + 4y? + 22 – 8x + 16y – 2z…

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Q: 7. Let fz) = z +1/z. Show that the level curve Imf(z) = 0 consists of the real axis (excluding z =…

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Q: (2) Let L be the line defined by 3 L(t) = 1 + and let p be the point (-1,6, 2). Find the minimal…

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Q: Let a and b be nonzero and f(x, y) = (ax + by)e-x Show that if a ± b, then there are five critical…

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Q: Let a, ßeR ,such that 2(a -1)+ 3(a – 1)+ 6a=0 and 2(1-B)+ 3(1-B)-6B + 12=0 and a + B, also graph of…

A:

Q: 3. The vertices of AFGH are F(-1, 1), G(-5, 4), and H(-5,-2). X is the midpoint of FG, and Y is the…

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Q: -6 3 Let y = -5 and u = -4 -2 Compute the distance d from 3y to the line through u and the origin.

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Q: 3 z 2 1 -2 -1 2

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Q: 6. Which of the following is true if OF dr 0 on all closed curves? (a) V×F = 0. (b) div F = V·F = 0.

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Q: Consider the following curves C1 : x³ + y³ = 1 C2 : z³ + y³ = 9 C3 : y= x+1 C4 : y = 0 that are…

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Q: A natural cubic spline is defined by if 0 < x < 1 12 + 36(x – 1) – 9(x – 1)² + 3c(x – 1)³ if 1 <x <…

A: Given: 'Natural Cubic Spline' is a piece-wise cubic polynomial that is twice continuously…

Q: (2) Let L be the line defined by 3 L(t) 1 1 = .4 and let p be the point (-1,6,2). Find the minimal…

A: Given: Let L be the line defined by  L(t)=31-4 + -215 t And p=(-1, 6, 2) We have to find the minimal…

Q: Consider the intersection curve C in the first octant, between the surfaces s1: 2 = 1- r? S2 : 2 +…

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Q: 18.7. Let f(z) = (e + e-2)/2. Evaluate f(2) dz, where is any simple closed curve enclosing 0. 18 8…

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Q: 8 -2 Let y = and u = 1 -6 Compute the distance d from y to the line through u and the origin. d =

A: Solution:

Q: Q5 (B) Let A = {1,2,3, 4, 5,7}. Draw the directed graphs associated with the following relations on…

A:

Q: 4. Show that the distance between the two points z1 and z2 in an Argand diagram is |z1 – z2). In…

A: (6) z-1=2 Given that:The points z=x+iy satisfies the condition z-1=2 The complex number z=x+iy…