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In Problems 27 –32, use Definition 1 to determine whether the functions
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Fundamentals of Differential Equations and Boundary Value Problems
- Determine which of the following pairs of functions are linearly independent. 1. f(x) = x² g(x) = 4|x|² NO_ANSWER NO_ANSWER NO_ANSWER NO_ANSWER " ✓ 2. f(x) = e4x ✓ 3. f(0) = cos(30) ✓ 4. f(t) = 3t, g(t) = |t| " g(x) = 4(x-3) 2 g(0) = 4 cos³ (0) - 4 cos(0)arrow_forward5. Prove that the functions ex, sin(x), cos(x) = F(R,R) are linearly independent.arrow_forwardSuppose that y is a function of u, u is a function of x, and u = -1 when x = 2. If du/dx|x=2 = 3 and dy/du|u=-1 = 5(dy/dx|x=2) + 1, then dy/du|u=-1 equals (a)9/25 (b) -3/14 (c) 11/14 (d) 29/14 (e) none of thesearrow_forward
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- 1 If f(x, y) = x² +y² find f, and f,.arrow_forward4) Find the Frenet (TNB) frame for the following function at the point (√3,-1,3π): r(t) = (2 sin(t).-2 cos (t), 3t) (Hint: once you find T and N, you can plug in the value of t before finding B since it doesn't involve taking a derivative!)arrow_forward1. The curve y = x2 – ax + b has turning point (1, 3). Find a and b. 2. Find the coordinates of the maximum and minimum points of the functions y = x3 – 2x2 + x - 7. 3. Evaluate 8x5 - 3x dx a. x3arrow_forward
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