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Calculus I Examination #2: Solutions for Sections I-VII, Exams of Calculus

Bharat Ratna Dr. B. R. Ambedkar UniversityCalculus

The solutions for examination #2 of mathematics 105 - calculus i. It includes the steps to solve problems related to initial value problems, calculating derivatives, finding limits, and optimization problems. Additionally, it covers using newton's method to find roots.

Typology: Exams

2012/2013

Uploaded on 03/21/2013

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NAME_____________________________________________________
I______ II______ III______ IV______ V______ VI______ VII______ TOTAL _______
(10) (20) (30) (10) (10) (10) (10) (100)
November 13 Mathematics 105 Mr. Haines
2009 Calculus I
Examination #2
(10) I. Solve the Initial Value Problem:
(i)
33
2
)2cos(
1
1
'exx
x
y+++
−
=
(ii)
0)0(
=
y
pf3
pf4
pf5

Partial preview of the text

Download Calculus I Examination #2: Solutions for Sections I-VII and more Exams Calculus in PDF only on Docsity!

NAME_____________________________________________________

I______ II______ III______ IV______ V______ VI______ VII______ TOTAL _______

November 13 Mathematics 105 Mr. Haines 2009 Calculus I Examination #

(10) I. Solve the Initial Value Problem:

(i) 2 3 cos( 2 )^3 1

' x x e x

y + + + −

(ii) (^) y ( 0 )= 0

(20) II. Calculate y ′^ if

A. y = 3 x cos( 5 x ).

B. y = sin( 2 x + 1 ).

(10) IV. Find the following limits. For full credit, show your work and explain your reasoning:

A.

x

x x 7 7

lim 3 −

B. (^) x x x 3

lim (^2) + 1 → ∞

(10) V. If x and y are positive real numbers whose product is 16, find the minimum value taken on by x + y^2.

(10) VII. Use Newton’s Method to try to find roots for f ( x )= x^2 + x + 1

A. The iteration function for f ( x )is

N ( x ) = ____________________________.

B. If the initial guess is x 0 = 1, compute the next three approximations:

x 1 = __________________________________.

x 2 = __________________________________.

x 3 = __________________________________.

x 4 = __________________________________.

C. Sketch a graph of y = f ( x )and explain why you get the approximations you do.