Suppose that you have three vectors: f1 (x) = 1, f2 (x) = x – 1, and f3 (x) = } (x² – 4x + 2), that make up an orthonormal basis spanning the real vector space of quadratic functions with the inner product: (f: | f;) = L° fi (x) f; (x) e¯²dx. Suppose we have a derivative operator D = . What is (fi |D| f3) =? -1 2 3/4

Q: the line (x/a)+(y/b)=1 moves in such a way that (1/a\power{2})+(1/b\power{2})=(1/c\power{2}) ,where…

A: Variable line is                xa+yb=1                 ......(1)Any line perpendicular to (i) and…

Q: Which of the following is not true for the differential operators A, B, and C? A (A+B) +C = A+ (B+C)…

A: Differential operator

Q: 2 Suppose that A = 3xyz²7 + 2xy³j - x²yzk and p = 3x² - yz. Find, at the point (1,-1, 1), 2.1 Vo,…

A:

Q: Calculate the derivative using Part 2 of the Fundamental Theorem of Calculus. & 1² (520 - €) 30 dt =…

A:

Q: 3) Show that the function 13-212+2 g(2) = is a Complex differontiable function ait the point 20 =1…

A:

Q: Minimizing the length of the residual vector r = b – Ax is equivalent of mini- mizing the quadratic…

A:

Q: Given the function g of the two real variables t and u by g(t,u)=t^2 + tu-u^2+(6+2)u c) Determine…

A: Linearization of a function g(t,u) about (a,b) is  L(t,u)=g(a,b)+(t-a)gt(a,b)+(u-b)gu(a,b)

Q: -3t k Compute the first, second, and third derivatives of r(t) = 3ti + 5 In(t)j + 5e

A: r(t)=(3t)i+(5lnt)j+(5e-3t)k   We are required to findFirst derivative Second derivativeThird…

Q: u = x² + y³ + z*, X = s•t = s2 +t2 y = z = s-t

A: We find complex function

Q: Exercise 6: Suppose f and g are functions such that: -3 f = 1, i=7, f = 5, -3 Г» g = 6, g = 3, :-4.…

A: Suppose f and g are functions such that

Q: Determine which of the following pairs of functions are linearly independent. NO_ANSWER f(x) =e5 "…

A:

Q: Find the gradient of cos(xy) – 3y4 + 3 at the point (1,4) -

A:

Q: Find the gradient of f(m, n) = m³ +n³. grad f = i +

A:

Q: derivative 2 of the Fundamental Theorem of Calculus. √²₁ (61²-1) 22 dt 6+2 dt (61²-1) 22 dit

A: Given query is to find the derivative.

Q: Find f '(2), where f(t) = u(t) v(t), ū(2) = (1, 2, -1), u' (2) = (3,0, 4), and v(t) = (t, t², t³).

A:

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.