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Practice Examination 1 - Calculus I - Fall 2002 | MAT 151, Exams of Calculus

Material Type: Exam; Professor: Thistleton; Class: Calculus I; Subject: Mathematics; University: SUNY Institute of Technology at Utica-Rome; Term: Fall 2002;

Typology: Exams

Pre 2010

Uploaded on 08/09/2009

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MAT321 Exam 1 October 2, 2002
Prof. Thistleton
1.
(a) Sketch a graph of f(x)=x23 and draw a line on your graph tangent to the curve at
the point (1,2).
−4 −3 −2 −1 0 1 2 3 4
−4
−3
−2
−1
0
1
2
3
4
(b) What is the slope of the secant line which intersects the graph at the points (1,2) and
(1 + x, f (1 + x))?
(c) By taking a limit as x0, calculate the slope of the tangent line through (1,-2) as
the limit of the slope of the secant line and find the equation for this line.
pf3
pf4
pf5

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MAT321 Exam 1 October 2, 2002 Prof. Thistleton

(a) Sketch a graph of f (x) = x^2 − 3 and draw a line on your graph tangent to the curve at the point (1, −2).

−4 −4 −3 −2 −1 0 1 2 3 4

0

1

2

3

4

(b) What is the slope of the secant line which intersects the graph at the points (1, −2) and (1 + ∆x, f (1 + ∆x))?

(c) By takinga limit as ∆ x → 0, calculate the slope of the tangent line through (1,-2) as the limit of the slope of the secant line and find the equation for this line.

(a) On the axes below, sketch the functions f (θ) = sin(θ) and g(θ) = 2sin(θ) for 0 ≤ θ ≤ 2 π.

− − (^32) − 1 0 1 2 3 4 5 6 7 8

− 2

− 1

0

1

2

3

(b) On the axes below, sketch the functions f (θ) = sin(θ) and g(θ) = −sin(2θ) for 0 ≤ θ ≤ 2 π.

− − (^32) − 1 0 1 2 3 4 5 6 7 8

− 2

− 1

0

1

2

3

(c) On the axes below, sketch the functions f (θ) = sin(θ) and g(θ) = sin(πθ) for − 2 ≤ θ ≤ 6.

− − (^32) − 1 0 1 2 3 4 5 6 7 8

− 2

− 1

0

1

2

3

  1. Sketch the graph of the function f (x) = | 3 x − 3 |

− − (^44) − 3 − 2 − 1 0 1 2 3 4

− 3

− 2

− 1

0

1

2

3

4

  1. Sketch the graph of the function f (x) = x x−+1^1

− − (^44) − 3 − 2 − 1 0 1 2 3 4

− 3

− 2

− 1

0

1

2

3

4

  1. Sketch the graph of the function f (x) = (^) x^12

− − (^44) − 3 − 2 − 1 0 1 2 3 4

− 3

− 2

− 1

0

1

2

3

4

  1. Calculate the followinglimits

(a) limx→3+ x x+1− 3

(b) limx→ 0 − |x x|

  1. Calculate the followingderivatives at the indicated points.

(a) f (x) = x + sin(x), at (x, y) = (0, 0)

(b) f (x) = 3x^2 + 2x − 5 , at (x, y) = (1, 0)