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The spring 2007 exam 1 for the mat 250 calculus course, focusing on limits and derivatives. Students are required to use the graph of a function, algebraic methods, and the intermediate value theorem to find limits, evaluate continuity, and determine instantaneous velocities. The document also includes a bonus question on exponential expressions.
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Spring ’07/MAT 250/Exam 1 Name: Show all your work.
lim x→ 3 −^
f (x) =
lim x→ 3 +^
f (x) =
lim x→ 0 f (x) =
lim x→− 2
f (x) =
Is f continuous at x = −2 and why (not)?
a) lim x→ 7
x^2 − 4 x − 21 x − 7
b) lim x→ 3
(x − 3)^2
3 x − 12 √ 8 x + 1 −
a) Use your calculator to estimate the limit with three accurate decimal places. Show the table of values. b) Find the limit algebraically and compare your answer to a).
2 + sin (^1) x. Use the theorem that rhymes with what an allergy
sufferer might do.
f (x) =
3 x − 2 , if x ≤ 2 12 − 4 x, if 2 < x.
f ′(a) =
f ′(b) =
f ′(c) =
Bonus. (5pts) Algebraically find the limit of the exponential expression
lim x→∞
x^3 +x+ x−x^2 =