Please answer all the questions showing work thanks

21. Given a magnetic field B=B0gt2y^, where B0 and g are constants, and an area vector of a coil A=NAy^, where N and A are constants, find an expression for the magnetic flux in terms of B0,g,N,A, and t. 2. Given a function f(x)=Dsin(mx), find df/dx, the derivative of f with respect to x. 23. Open the Desmos link given above. Vary each of B0,N,A, and . How does changing each of these values affect the induced EMF, E ? 24. Set the values of B0,N,A, and to be their values from the exam. (Note that you will probably have to type these values in by hand and re-adjust the scale of the axes afterwardszoom in or out until you can see several cycles of the cosine wave.) Leave =0 for now. What is the maximum value of the induced EMF, E ? 25. Vary , the angle between B and A. How does changing change the induced EMF? What value of leads to the smallest possible induced EMF? What value of produces an induced EMF which is exactly opposite the induced EMF for =0