Construct a cubic spline that interpolates sin x at nodes 0, T/2, T, 37/2, 27 (use the true derivative of cos x to supply extra endpoint conditions). Write down its expression on each piece.

Q: y = [x+ (x + ¯ sin² 3x)°]

A:

Q: y=(2√√x-3)(6-5x²)

A: y=2x-36-5x4

Q: If sinX = -1/3 and cosX is positive, determine the exact value of cotX.

A: We know, cosx= ±√(1-sin2x) cotx= cosx/sinx

Q: Use implicit differentiation to solve the following questions.  x^2-2xy+5y^2=6

A: Given:- x2 - 2xy+5y2=6 To find:- Use implicit differentiation to find dy/dx

Q: Find the derivative of each function: 2x+3 y = Зх +2 а. b. y =x sin 2x tan x c. y = e" d. x² +xy+ y…

A: we have to find the derivative of each of function

Q: Make each derivative by any method. Thanks

A:

Q: 4. y = sin 2x 1-cos 2x

A: We have to find the derivative of

Q: Verify: 1. (sinx – cosx)² – 1 = -sin2x %3D

A: We can verify the statement as below