Question

Find the mean rate of change of the following functions in the interval $[1,2]$ :- i. $\quad f(x)=x^{2}$. \{Ans. 3\} ii. $\quad f(x)=x^{3}$. \{Ans. 7$\}$ iii. $f(x)=\sqrt{x}$. \{Ans. 0.414\} iv. $\quad f(x)=\frac{1}{x} .$ \{ns. $\left.-0.5\right\}$ v. $\quad f(x)=e^{x}$. \{Ans. 4.67\} vi. $f(x)=\ln x .\{$ Ans. $0.693\}$ vii. $f(x)=\sin x .\{$ Ans. $0.068\}$ viii. $f(x)=\cos x$. \{ns. $-0.956\}$

Name: Problem 1, Chapter 5: Mathematics for IIT JEE Main and Advanced Differential Calculus Algebra Trigonometry
Uploaded: 2021-07-26T11:50:18-08:00
Duration: 4 min 13 s
Channel: Nidhi Singhi
Description: Find the mean rate of change of the following functions in the interval [1,2] :- i. f(x)=x^2. {Ans. 3} ii. f(x)=x^3. {Ans. 7} iii. f(x)=√(x). {Ans. 0.414} iv. f(x)=(1)/(x) . {ns. .-0.5} v. f(x)=e^x. {Ans. 4.67} vi. f(x)=lnx .{ Ans. 0.693} vii. f(x)=sinx .{ Ans. 0.068} viii. f(x)=cosx. {ns. -0.956}

   Find the mean rate of change of the following functions in the interval $[1,2]$ :-
i. $\quad f(x)=x^{2}$. \{Ans. 3\}
ii. $\quad f(x)=x^{3}$. \{Ans. 7$\}$
iii. $f(x)=\sqrt{x}$. \{Ans. 0.414\}
iv. $\quad f(x)=\frac{1}{x} .$ \{ns. $\left.-0.5\right\}$
v. $\quad f(x)=e^{x}$. \{Ans. 4.67\}
vi. $f(x)=\ln x .\{$ Ans. $0.693\}$
vii. $f(x)=\sin x .\{$ Ans. $0.068\}$
viii. $f(x)=\cos x$. \{ns. $-0.956\}$

Mathematics for IIT JEE Main and Advanced Differential Calculus Algebra Trigonometry

Sanjiva Dayal IIT… 1st Edition

Chapter 5, Problem 1

Instant Answer

Solved by Expert Nidhi Singhi

07/26/2021

Step 1

In this case, $a = 1$ and $b = 2$. Show more…

Show all steps

Thanks for your feedback!

Find the mean rate of change of the following functions in the interval $[1,2]$ :- i. $\quad f(x)=x^{2}$. \{Ans. 3\} ii. $\quad f(x)=x^{3}$. \{Ans. 7$\}$ iii. $f(x)=\sqrt{x}$. \{Ans. 0.414\} iv. $\quad f(x)=\frac{1}{x} .$ \{ns. $\left.-0.5\right\}$ v. $\quad f(x)=e^{x}$. \{Ans. 4.67\} vi. $f(x)=\ln x .\{$ Ans. $0.693\}$ vii. $f(x)=\sin x .\{$ Ans. $0.068\}$ viii. $f(x)=\cos x$. \{ns. $-0.956\}$

Play audio

Feedback

Nidhi Singhi and 64 other subject Calculus 1 / AB educators are ready to help you.

Ask a new question

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Difference Quotient

The difference quotient is the expression used to calculate the mean rate of change. It is given by the formula (f(b) - f(a)) / (b - a), where a and b are the endpoints of the interval. Analyzing this quotient helps to determine the average slope of the function over the interval, thereby providing insight into the function's behavior and its rate of change over that specific interval.

Mean Rate of Change

The mean rate of change of a function over an interval is a measure that represents the average change in the function's output per unit change in the input. It is calculated by taking the difference in the values of the function at the endpoints of the interval and then dividing by the difference in the input values. This concept is fundamental in understanding how functions behave between two points and forms a basis for the concept of derivatives in calculus.

Please give Ace some feedback