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Engineering Mathematics Through Applications

Kuldeep Singh

Chapter 7

Engineering Applications of Differentiation - all with Video Answers

Educators

Section 1

Curve sketching

05:10

Problem 1

Obtain the stationary points for the following functions:
a $y=x^{2}+3 x+1$
b $y=x^{3}-3 x$
c $y=\frac{x^{3}}{3}-x$
d $y=x^{2}\left(50-x^{2}\right)$

Jennifer Stoner
Jennifer Stoner
Numerade Educator
03:33

Problem 2

[mechanics] The trajectory of a projectile is related by
$$
y=\frac{10 x-x^{2}}{10}
$$
where $x$ and $y$ are the horizontal and vertical displacement components respectively. Sketch the graph of $y$ against $x$.

Daphne Pusey
Daphne Pusey
Numerade Educator
01:22

Problem 3

Find the maximum and minimum points of $y=x^{3}+x^{2}-5 x$

AG
Ankit Gupta
Numerade Educator
03:14

Problem 4

The displacement, s, of a particle is given by
$$
s=t^{3}-6 t^{2}+12 t
$$

Zulfiqar Ali
Zulfiqar Ali
Numerade Educator
07:49

Problem 5

The displacement, s, of a particle moving along a horizontal line at time $t$ is given by
$$
s=t^{2}\left(8-t^{2}\right)
$$
Sketch the graph of $s$ against $t$.

Kush Khamesra
Kush Khamesra
Numerade Educator
03:54

Problem 6

The energy, $w$, of an inductor at time $t$ is given by
$$
w=1-\cos (50 t)
$$
Sketch the graph of $w$ against $t$ for $0 \leq t \leq \frac{\pi}{25}$

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
01:38

Problem 7

The power, $p$, in a resistor is given by
$$
p=10 \sin ^{2}(t) \text { where } 0 \leq t \leq 2 \pi
$$
Sketch the graph of $p$ against $t$, marking all the points of maximum, minimum and inflexion.

Carl David Cepeda
Carl David Cepeda
Numerade Educator
01:04

Problem 8

The energy, $w$, absorbed by a resistor at time $t$ is given by
$$
w=5 \sin (2 t)+10 t
$$
Sketch the graph of $w$ against $t$ for $0 \leq t \leq 2 \pi$

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
01:00

Problem 9

The power, $p$, of an inductor is given by
$$
p=\left(t^{2}-2 t\right) e^{-2 t} \quad(t \geq 0)
$$
i What is the value of $p$ as $t$ gets large, $t \rightarrow \infty ?$
ii At what values of $t$ is $p=0 ?$
iii Find the minimum value of $p$.
iv Find the maximum value of $p$.
v Sketch the graph of $p$ against $t$ for $t \geq 0$

Raj Bala
Raj Bala
Numerade Educator
01:12

Problem 10

The current, $i$, through a circuit is given by
$$
i=5 t e^{-5 t} \quad t \geq 0
$$
I What is the value of $i$ for large $t$, $t \rightarrow \infty ?$
ii Find the maximum current through the circuit.
iii Sketch the graph of $i$ against $t$ for $t \geq 0$

Khushbu Rani
Khushbu Rani
Numerade Educator