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- = Either f,g,h € F(R, R) the functions f(x) sin(x)^2 And g(x) = cos(x) and h(x) = sin(x). Show that f, g and h are linearly independent =arrow_forwardOW + OW = 0 for w = f(x, y), x = u – v, and y = v –- u and demonstrate the ди ду 6. Show that result for w = (x – y) sin (y – x).arrow_forwardSketch the graph of the vector-valued function r(t) = (2t – 1)² î + (2t +2) ĵ. Draw arrows on your graph to indicate the orientation.arrow_forward
- Let f (x, y) and g(x, y) be functions of two variables withthe property that ∂ f/∂x= ∂g/∂x and ∂ f/∂y= ∂g/∂y for every point(x, y) ∈ R2. What is the relationship between f and g?arrow_forwardAnother derivative combination Let F = (f. g, h) and let u be a differentiable scalar-valued function. a. Take the dot product of F and the del operator; then apply the result to u to show that (F•V )u = (3 a + h az (F-V)u + g + g du + h b. Evaluate (F - V)(ry²z³) at (1, 1, 1), where F = (1, 1, 1).arrow_forwardIf W(f, g) = sin t then the functions f , g are linearly independent Select one: O True O Falsearrow_forward
- make v the subject 1/f=1/u+1/varrow_forwardOnly 3.2 and 3.3 pleasearrow_forwardEvaluate this function of z = cos x sin y; x = u – v, y = u? + v². Use chain rule to find Oz ди А. 2ucos (u – v) cos (u? + v²) – sin(u – v) sin (u² + v²) В. 2usin (u – v) cos (u? + v² ) – cos(u – v) sin(u² + v²) - - - С. 3ucos (u – v) cos (u? + v²) + sin(u – v) sin(u² + v² ) D. 3usin (u – v) sin(u? + v²) + cos(u – v) sin (u² + v²) -arrow_forward
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