Consider the functions fi(x) = x and f2(x) = 5-9cx on the interval [0, 1]. (a) Find the value of the constant c so that fi and f2 are orthogonal on [0, 1]. (b) Using the value of the constant c from part (a), find the norm of f2 on the interval [0, 1].

Q: Let L be the line passing through the point P(1, 1, 1) with direction vector d=[2, 1, 0]T. Find the…

A:

Q: Find the domain of the vector function r(t)=⟨ln⁡(19t),sqrt(t+8),1/sqrt(7−t)⟩ using interval…

A: Given vector function isrt=ln19t,t+8,17-tfind the domain.

Q: Suppose that f: R² R² is a function such that f (1,2)= the linear approximation. (Use syntax like…

A: We have to estimate f (1.1, 2.01) using the linear approximation.

Q: (c) If f is a C² scalar function, then V × (Vƒ) = 0. True False (d) The lines 1₁ (t) = (1 − t, 1+ t,…

A: (C) If c is scalar function Means      curl(grad ƒ)  is = 0   Therefore correct ans is  True

Q: Show that (u - v) × (u + v) = 2(u × v)

A:

Q: Find the derivative of the vector function r(t) = ta x (b + tc), where a = (-5, −1, −1), b = (−2,…

A:

Q: Suppose that f: R² → R² is a function such that f (1, 2) = the linear approximation. (Use syntax…

A:

Q: ΣΣ-ΣΣ-Σ j=1

A: To Explain: How ∑i=1k+1    ∑j=1i1=∑ i=1k    ∑j=1i1+∑j=1k+11

Q: Use Taylor's theorem to obtain an upper bound for the error of the approximation. Then calculate the…

A: We have cos0.4=1-0.422!+0.444! We have to find  R4≤                       R4=

Q: Find the domain of the vector function T (ty= Vt + 7 Domain: {t <t< }

A:

Q: R(t) = = {{In(3 In(3 – t), (0, -1, 4), 4t-8 4-t2⁹ 8), 3t² – 8 t#2 t = 2.

A:

Q: 3 - Find the Derivatives of the following Vectors, Where F(t)* = 2secti – 3j* + csctk and G(t)* =…

A:

Q: d) Let g(x,y) = (3x + y)2(2y + 1) and h(x, y) = 6y2(2x + y) h i) Find дх’ ду’ дх’ ду

A: The given functions are  and

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:

Q: consider the vector-valued function r(t) = a) State the domain of r(t) b) Identify where r(t) is…

A: