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Calculus Exam: Graphing, Derivatives, and Limits - Prof. William Thistleton, Exams of Calculus

A calculus exam focusing on graphing functions, finding tangent lines, calculating derivatives, and determining limits. The exam covers various functions such as trigonometric, polynomial, and quadratic equations.

Typology: Exams

Pre 2010

Uploaded on 08/09/2009

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MAT321 Exam 1 24 February, 1999
Prof. Thistleton
(1) Sketch a graph of
f
(
x
)=1
=
(
x
1). Calculate the equation of the tangent line through (2,1) and include this
line on your graph.
pf3
pf4
pf5

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MAT321 Exam 1 24 February, 1999 Prof. Thistleton

(1) Sketch a graph of f (x) = 1 =(x 1). Calculate the equation of the tangent line through (2,1) and include this

line on your graph.

(2) Calculate the following derivatives:

1. d dx x^3 + 5 x^2 + 2 x + 1

2. d dx sin(x)cos(x)

  1. d dxx

(^2) + x^2 1

4. d dx sin(x^3 + 1)

5. d dx cos^2 (x^5 )

(4) On the axes b elow, sketch the functions f ( ) = sin( ) and g ( ) = sin( =2). for 0    2 .

On the axes b elow, sketch the function f (x) = (x 1)=(x + 1). Calculate the limit of this function as x! 1 +^.

(5) Calculate the following limits

lim x! 4

p

x^2 + 9 5

x 4

lim x! 1

x^3 1

x 1

Calculate the equation of the line tangent to the graph of

x^2

y 2

at the p oint (5,3).