Problem 5. Let a E R" be fixed. Suppose that vectors x, y E R" are related by the equation a = x+ (x· y)y. (a) Show that ||a||2 – ||x||? 2 + ||y||? (x ·y)² (b) Deduce that ||a|| > ||x||.

Q: Graph the function. 10) y = sec (2x - )+ 2 A) B) 3n x 2 C) D) Зл х 2.

A: graph the function

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Q: Which of the following is the reciprocal of a linear function? O a) f(x) = b) f(x). = 6 2x + 1 1 x²…

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Q: Which function has an x-intercept of - O a) f(x) = 3x + 2 5x-1

A: Introduction: The value of the x-coordinate at the point where the graph intersects the x-axis, or…

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A: Given: f(z)=z5+1

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Q: a z = 4x³-6x²y²-y com x= 2sen(t) y=-3cos(t) e

A: #As per the guidelines we are entitled to solve one question at a time, please resubmit the other…

Q: 3. Which function has a range of yS 3? Ax) -- +3 с. a.

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Q: + y = 2. What is y" at the point (1, 1)? y ² Suppose that x +

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Q: A function is defined as f(x,y) = 25xy + 3x³ - 7x² sin(y) aj ay a2f (ii) Find and 1325 3²x (iii)…

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Q: Which graph corresponds to the function given? h(x) = {x², x 1

A: Here we have to draw the graph of the function.

Q: Question 3 Let f(z) 2r-3z2-6z+2. Find the the equations of all tangent lines to f which are parallel…

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Q: 5. State the domain and range of each function. a) y = 2x- 1 b) y = -3(x – 4)² + 1 c) y d) y = V-3(x…

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Q: What is the y-intercept for f(x) =;|2x + 6| – 1? А. (2,0) В. (о,-2) C. (0,6) D. (0,-1) E. not given

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Q: 9) Find a linear function of the form f(x) = ax +b that satisfy the conditions A-4) = 8 and (3) - 9.

A: f(x) = ax+bf(-4) = 8→ -4a+b = 8.........................1f(3) = 9→3a +b =…

Q: Question 3 Let f(x) = 2x³ – 3.x2 – 6x + 2. Find the the equations of all tangent lines to f which…

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Q: If i = xi+yi+zk then grad (r") is equal to

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Q: If B = x°ya, + (2x + y)a, – (y – 2)a, find (a) V B (b) V X B (c) V (V B) (d) V x V X B

A: Given : B=x2yax +(2x2+y)ay - (y-z)az

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Q: 2 f: TR² x R² → R f (x, y) = 1 (2ax₁ y₁ + bx₁ y₂ + bx₂y₁ +2Cx₂4₂) 2 Examine whether the function is…

A: Given :   fx , y =122ax1y1 + bx1y2 + bx2y1+2cx2y2 To check : whether  f(x ,y) is 2 - linear  and…

Q: 4 y-fx) 36) Use the graph of the quadratic function to write it as: f(x)-a(x -h)'+k 26 -4-2

A: The graph is downwards parabola whose equation is (y-k)=a(x-h)^2, where (h,k) is the vertex of…

Q: 6. Simplify the follow (1) D-A B C+.

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

Q: 5. Prove that xdx a b²_a² 2

A: According to guidelines we are supposed to do first question only. Kindly repost the other question.

Q: Question 3 Evaluate (-t, t, -2t)|| dt. 5

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