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Lecture Notes for MATH 1205 - Calculus with Glynn at Virginia Tech (VT)

Notes Information

Material Type:Note 2
Professor:Glynn
Class:MATH 1205 - Calculus
Subject:Mathematics
University:Virginia Polytechnic Institute And State University
Term:--
Keywords:
  • Differentiable
  • Test Questions
  • Trigonometric
  • Differentiation
  • Reference Angle
  • Product Rule
  • Speed Function
  • Inverse Sine
  • Quotient Rule
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Review Sheet 1205 Test 2 1. Derivatives: l' (x) = lim J(x + h) - J(x) if the limit exists. h-->O h We evaluated this limit in several ways: tables reading from the graph defmition rules ~ A function is differentiable if the derivative exists. A derivative does not exist: at a corner or sharp peak where there is a vertical tangent at a discontinuity ~ Iff is differentiable at c then f is continuous at c. Section 2.8 - 3.7, Worksheets 3-6 Since this limit is a rate of change it can give us instantaneous velocity: If s = J(t) is the position fctn with respect to time, then . J(t + At) - j(t). . v(t) = S' (t) = hm IS velOCIty M-V I1t speed = Iv(t) I a( t) = v' (t) is acceleration ~'-__ " I (~') We can use this information in many ways: Make decisions like the following: particle is momentarily at rest (that is, changing directions) when s'C t) = 0 particle is moving to the right when s'C t) + particle is moving to the left whens'(t)- particle is speeding up w...
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