Docsity
Docsity
Prepare for your exams
Prepare for your exams

Study with the several resources on Docsity

Earn points to download
Earn points to download

Earn points by helping other students or get them with a premium plan

Guidelines and tips
Guidelines and tips
Sell on Docsity
Sell on Docsity
Docsity AI
Docsity AI
Log inSign up

Prepare for your exams

Study with the several resources on Docsity

Find documents

Prepare for your exams with the study notes shared by other students like you on Docsity

Search for your university

Find the specific documents for your university's exams

Docsity AINEW

Summarize your documents, ask them questions, convert them into quizzes and concept maps

Explore questions

Clear up your doubts by reading the answers to questions asked by your fellow students

Earn points to download

Earn points by helping other students or get them with a premium plan

Share documents
download point icon20 Points

For each uploaded document

Answer questions
download point icon5 Points

For each given answer (max 1 per day)

All the ways to get free points
Get points immediately

Choose a premium plan with all the points you need

Study Opportunities

Choose your next study program

Get in touch with the best universities in the world. Search through thousands of universities and official partners

Community

Ask the community

Ask the community for help and clear up your study doubts

Free resources

Our save-the-student-ebooks!

Download our free guides on studying techniques, anxiety management strategies, and thesis advice from Docsity tutors

Calculus I Fall 2001 Homework: Derivatives, Limits, and Tangent Lines, Exams of Calculus

Birla Institute of Technology and ScienceCalculus

A calculus i homework assignment from fall 2001. The assignment covers topics such as finding derivatives of various functions, estimating limits, determining continuity, finding equations of tangent lines, and using the definition of the derivative. Students are required to 'justify your answers!!'

Typology: Exams

2012/2013

Uploaded on 03/15/2013

badsha
badsha 🇮🇳

4.3

(28)

213 documents

1 / 4

Toggle sidebar

This page cannot be seen from the preview

Don't miss anything!

bg1
Name:
Student Number:
Calculus I, Fall 2001
Justify your answers!!
(1) Find the derivatives of the following functions:
(a) f(x) = x3+3
√x
(b) f(x) = x6+x2
x
(c) f(x) = (x+ 1)2
(d) f(x) = x3ex
(e) f(x) = x3+√x
ex
(f) f(x) = (x+1)(x−1)
x2+1
1
pf3
pf4

Partial preview of the text

Download Calculus I Fall 2001 Homework: Derivatives, Limits, and Tangent Lines and more Exams Calculus in PDF only on Docsity!

Name:

Student Number:

Calculus I, Fall 2001

Justify your answers!!

(1) Find the derivatives of the following functions:

(a) f (x) = x

3

  • 3

x

(b) f (x) =

x^6 +x^2 x

(c) f (x) = (x + 1)^2

(d) f (x) = x^3 ex

(e) f (x) =

x^3 +

√ x ex

(f) f (x) =

(x+1)(x−1)

x^2 +

1

(2) Given the graph of the function y = f (x) below, estimate (or state DNE) :

(a) limx→− 2 f (x) =

(b) limx→− 1 f (x) =

(c) f

′ (−1)

(d) f ′(2)

(e) State where the function y = f (x) is NOT continuous.

(3) Find the equation of the tangent line to the graph of the function y = 3x^5 + 2x + 4

x

at x = 1.

(6) (a) Find the linear approximation of the function y = f (x) = ex^ at the point a = 0.

(b) Use this linear approximation to find an approximate solution to the equation

e

x = 100x.

(7) Given the graph of the function y = f (x) below, draw a reasonable graph of its

anti-derivative.