Maths for Electronics 1 End Term: 24 December 2023, Set AEF3 (September 2023 term)

Which of the following option(s) is (are) true?

Find the limit of the sequence {2an}.

If $a\pi^2$ is the volume obtained by revolving $f(x)$ about the $x-$axis from $x = 0$ to $x = 1$, then find the value of $2a$.

Hint:

$\int \frac{1}{\sqrt{x(1-x)}}\, dx = \sin^{-1}(2x - 1) + c.$

If $a\pi$ is the arc length of curve $g(x)$ between $x = 0$ to $x = \frac{1}{2}$, then find the value of $2a$.

Hint:

$\int \frac{1}{\sqrt{x(1-x)}}\, dx = \sin^{-1}(2x - 1) + c.$

What is the value of 20a?

The voltage across a capacitor in a circuit is governed by the first-order linear ordinary differential equation:

$\frac{dv}{dt} + \frac{v}{RC} = 20,$

where $v(t)$ is the voltage across the capacitor, $R$ is a resistance, $C$ is the capacitance, and $t$ is time.

Based on the above data, answer the given subquestions.

Let the time constant RC = 1. Which plot represents v(t) correctly?

The voltage across a capacitor in a circuit is governed by the first-order linear ordinary differential equation:

$\frac{dv}{dt} + \frac{v}{RC} = 20,$

where $v(t)$ is the voltage across the capacitor, $R$ is a resistance, $C$ is the capacitance, and $t$ is time.

Based on the above data, answer the given subquestions.