Determine which of the following pairs of functions are linearly independent. NO ANSWER + 1. f(x) = x² , g(x) = 4|x|2 NO ANSWER * 2. f(1) = ed"cos(Ht) g(1) = eA"sin(ut) ,u #0 NO ANSWER 3. f(0) = cos(30) g(6) = 2 cos (8) – 2 cos(8) %3D %3D NO ANSWER + 4. f(t) = 3t g(t) = |t|

Q.5 Show that both of the functions f(x)=(x-1) and g(x)=x – 3x +3x-2 have stationary points at x = 1.What does the first and second derivative test tell about the nature of these stationary points?

4. Find the a. y = x² sin x b. y = ex cos x 3 c. y = (x² + 1)^¹ (²-1) ²³ 2x+1 d. y = e. y = derivative of the following functions: x²-4 5x+1 2√√x-1

cos(2x) cos(6y) satisfies the Determine the value of a for which the function F(x,y) equation Fr – aFy = 0. 8.