show steps and explain 9) Determine the value of ... S" (3 sin(x) - 2 cos(x))...
3. Give P an inner product structure by defining (f,9)-of(ag(x)e"da (you do not have to show that this is an inner product). Apply the Gram-Schmidt process to (1, , ) with this inner product. Show your work. Hint: You may want to use the fact that Jooz"e-xdz = nl, which follows from n application of integration by parts. (You do not have to show this.) Fun Fact: The polynomials you find here are the first three Laguerre Polynomials, and are...
4. (a Let (sin( x cos( ) dr + (x cos(x + y) - 2) dy. dz= Show that dz is an exact differential and determine the corresponding function f(x,y) Hence solve the differential equation = z sin( Cos( y) 2 x cos( y) dy 10] (b) Find the solution of the differential equation d2y dy 2 y e dx dæ2 initial conditions th that satisfi 1 (0) [15] and y(0) 0
4. (a Let (sin( x cos( ) dr...
If sin(x) = and cos(x) < 0 and 0 (5) and sin⑨ x < 2T. determine the exact value of cos
If sin(x) = and cos(x)
Linear Algebra. Please show all steps.
3. Use the Gram-Schmidt process to construct an orthogonal basis of the subspace of V = CⓇ [0,1] spanned by f(0) = 1, g(x) = x, and h(x) = e" where V has the inner product defined by < 5,9 >= S f(x)g(x)da. TI 11
(In2)2 +1 -2 sin r+ (In 2)2 cos x Evaluate /2 cos z da In 2 2° cos x + 2° sin (In 2) ln 2 1 +ln2 ln2 (In 2)
(In2)2 +1 -2 sin r+ (In 2)2 cos x Evaluate /2 cos z da In 2 2° cos x + 2° sin (In 2) ln 2 1 +ln2 ln2 (In 2)
Determine the global extrema of f(x) = 2 cos x + sin 2x on [0, 1]. . 4x Determine the global extrema of g(x) = - 24 on [0, 2] Determine the global extrema of f(x) = In(x2 + 2) on (–1, 2]
Show how [sin((x+0.5)theta) - sin((x-0.5)theta)] / [2sin(theta/2)] = cos(x theta) Please show all steps clearly. Please do not overlook the theta in two places in the numerator.
cos 5x 2. Please verify that sin5x Sin x = 4COS 2x cosx 3). Kindly draw the graph of each function. ). Find and show the x and y intercepts. Find and show all asymptotes, if they eatest a). f() =-3X +9 b) g®) = (x+3)(x+2). c) h) = x+3x –10 d). f®) = 3 log2 (x +4)-1 e). M(x) = -4 sin (3x-7)+ 7 (oeier x-1 L Vaa
4. Show that the value of | cos(x)dx cannot be 2. 0 sin(x))
11. -1 points SAlgTrig4 7 1037 Verify the identity. sin(x) cos(-x) -sin x -cos x This answer has not been graded yet. Need Help? Rea I 12. O1 points SAgTrig4 7.1.040 Verify the identity. (sin(x) + cos(x))1 +2 cos(x) sin(x) This answer has not been graded yet Need Help? 16.0/1 points SAlgTrig4 7 1.063 Verify the identity csc(x) + sec(x) = cos(x) + sin(x) cot(x) + tan(x) .This answer has not been graded yet Need Help? Red 19. -1 points...