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

Download Calculus Exam: Graphing, Derivatives, and Limits - Prof. William Thistleton and more Exams Calculus in PDF only on Docsity!

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)

3. 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).