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Material Type: Exam; Professor: Thistleton; Class: Calculus I; Subject: Mathematics; University: SUNY Institute of Technology at Utica-Rome; Term: Fall 2002;
Typology: Exams
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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
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(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
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(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
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(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
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− − (^44) − 3 − 2 − 1 0 1 2 3 4
− 3
− 2
− 1
0
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− − (^44) − 3 − 2 − 1 0 1 2 3 4
− 3
− 2
− 1
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− − (^44) − 3 − 2 − 1 0 1 2 3 4
− 3
− 2
− 1
0
1
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(a) limx→3+ x x+1− 3
(b) limx→ 0 − |x x|
(a) f (x) = x + sin(x), at (x, y) = (0, 0)
(b) f (x) = 3x^2 + 2x − 5 , at (x, y) = (1, 0)
