# Question-   LO4: Examine how differential and integral calculus can be used to solve engineering problems. a- If two resistors with resistances R1 and R2 are connected in parallel as shown in the figure below, their electrical behaviour is equivalent to a re…

Solution-

LO4: Examine how differential and integral calculus can be used to solve engineering problems. a If two resistors with resistances R1 and R2 are connected in parallel as shown in the figure below, their electrical behaviour is equivalent to a resistor of resistance R such that \$= 2 + 2. If R1 changes with time at a rate r= “= and R2 is constant, express the rate of change Sof the resistance of R in terms of = R1 andR2. If an object with a speed v giving by the equation v(t) =1+4t+3¢? where tis the time taken to move per minute, what is the travelled distance during the third minute? Aire of mild steel has a radius of 0.5 mm and a length of 3 m. If the young modulus Y = 2.1.x 10" N/m? and the wire is stretched by a force of 40 N determine: 1- The longitudinal stress 2- The longitudinal strain 3- The elongation

1- The longitudinal stress 2- The longitudinal strain 3- The elongation e If the switch ‘Sis at position ‘1’ sufficiently long enough before it is moved to position ‘2’ and after this it is kept in position 2 as shown in the figure below determine: + Values of the instantaneous inductor voltage v, and the instantaneous current through the inductor i, 2 Values of the inductor voltage v, and the current through the inductor i, just after the switch changes 3 The rate of change of i, at t=0 10a TC » e If the equation y = x3— 6 x? + 9x Find the stationary points of the curve and determine whether these points are maxima or minima and prove this.

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