Please explain your answer clearly.


Please explain your answer clearly. 4. Use the Fundamental Theorem of Calculus to find v(t) and...
8. (10 marks) Verify Stokes' Theorem for F = x?i + xyj + zk, where S is the part of the sphere x2 + y2 + z2 = 1 for z > 0.
Find the inverse Laplace transform, f(t) of the function F(s)+ f(t) Points possible: 1 S > 3 Preview t>0 Enter an algebraic expression [more..]
3. Use the mean value theorem to prove the following inequality. (1 +x)" >1 for z >0 andnEN
Question 4 Find i(t) for t >0 for the circuit below. 4Ω 12 V 5 H 3 A
step by step please, thank
you
(2) Use Stokes' Theorem to evaluate the integral F.dr, where F(x, y, z) =< -Y, I, z > and where S is the upper hemispherical surface defined by z = v1- 2 - y2. The boundary of S is the curve C defined by Cos (t) y= sin (t) 0t 27 Z=0
Use the differential equation approach to find Vo(t) for t> 0 in the circuit in the figure below 1k0 Please round all numbers to 3 significant digits. Vo(t)
4. Use the Fundamental Theorem for Conservative Vector Fields to compute F. dr. where F= <3y2 - 4x3y3,6xy - 3x*y2 > and C is parametrized by r(t) = < e. +9 > from t = 0 to 1= 2.
(2) The circuit is at steady state for t<0. Find v(t) for t>0. Answer t=0 ZF Navt)14 T
(1 point) Use Part I of the Fundamental Theorem of Calculus to find the derivative of cos(t2+t)dt n'(z) =
(1 point) Use Part I of the Fundamental Theorem of Calculus to find the derivative of cos(t2+t)dt n'(z) =
Find vo(t) for t > 0 Q#3 and
Q#4
3. Find vo(t) for t0 4 H 2Ω 4Ω 4 A Answer: vo(t)4e2t [At 0 4. Find i(t) for t> 0 5 mA 1 mH Answer: it) -5e7.5*10°1 [mA] t20