• Home
  • Textbooks
  • Engineering Mathematics Through Applications
  • Differentiation

Engineering Mathematics Through Applications

Kuldeep Singh

Chapter 6

Differentiation - all with Video Answers

Educators

Section 1

The derivative

01:21

Problem 1

Find $\frac{\mathrm{d} y}{\mathrm{~d} x}$ of the graphs shown below in Fig. 12:

Joseph Liao
Joseph Liao
Numerade Educator
04:13

Problem 2

[structures] The bending moment, $M(\mathrm{kN} \mathrm{m})$, of a beam of length $8 \mathrm{~m}$ is given by
$$
M= \begin{cases}2.16 x & 0 \leq x<5 \\ 28.8-3.6 x & 5 \leq x \leq 8\end{cases}
$$
where $x$ is the distance along the beam. The shear force, $V$, is given by $V=\frac{\mathrm{d} M}{\mathrm{~d} x}$. Sketch $V$ for $0 \leq x \leq 8$

Surendra Kumar
Surendra Kumar
Numerade Educator
03:30

Problem 3

through an inductor is given by
$$
i= \begin{cases}t & 0 \leq t \leq 2 \\ 4-t & 2<t \leq 4\end{cases}
$$
Sketch the current $i$.
The voltage, $V$, applied across the inductor is given by $V=0.25 \frac{\mathrm{d} i}{\mathrm{~d} t}$.
Sketch the voltage, $V$, on different axes.

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
03:55

Problem 4

applied across an inductor of inductance $L$ is
$$
V=L \frac{\mathrm{d} i}{\mathrm{~d} t}
$$where $i$ represents the current through the inductor. If the current $i$ is as shown in Fig. 13, find $V$.

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
06:10

Problem 5

By using the definition $6.1$, find $\frac{\mathrm{d} y}{\mathrm{~d} x}$ for the following:
a $y=x$
b $y=5 x$
* c $y=x^{2}+x$
d $y=\frac{1}{x}$

Md. Tajrian Taher
Md. Tajrian Taher
Numerade Educator
01:04

Problem 6

i Plot the function $y=10 x^{6}$ for $x=0$ to 3
ii Plot on different axes the function $y=10 x^{6}$ for $x=1.4$ to $1.6$ $x=1.49$ to $1.51$ and $x=1.499$ to $1.501$.
iii Evaluate $\lim _{h \rightarrow 0} \frac{10(1.5+h)^{6}-10(1.5)^{6}}{h}$.
This is $\frac{\mathrm{d} y}{\mathrm{~d} x}$ of $y=10 x^{6}$ at $x=1.5$.

Dwijendra Rao
Dwijendra Rao
Numerade Educator