**Exam 1 Review Topics**

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**Basics: **concept of limit, left and right limit;
definition of continuity; tangent line, secant line; concept of average and
instantaneous slopes/velocities; definition of derivative, rate of change,
slope of curve, second and higher order derivatives, acceleration

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**Techniques: **find limits by numerical and graphical
means using graphical calculator; find limits of undetermined types: ∞/∞,
0/0; find limits of rational functions, linearity rule; find roots of
polynomials through factorization; finding derivative by definition;
derivatives of elementary functions including polynomials, exponential
functions, and trigonometric functions; differentiation rules: linearity rule,
product rule, quotient rule, chain rule, and implicit differentiation; find
equations of tangent lines and sketch tangent lines; sketch the derivative
function f ’(x) if the function f(x) is given and vice versa; sketch the second
derivative function f’’(x) if f(x) or f’(x) is given and vice versa; find
intervals of increasing and decreasing; find intervals of concave up and
concave down; hand sketch lines, parabola, cubic functions, trigonometric
functions with different periods, exponential functions, trigonometric
functions with varying amplitudes

**Elementary Functions:** basic forms and shapes of
polynomials: linear function, parabola, cubic polynomials; definitions of
trigonometric functions; exponential functions, log functions and their
algebraic properties and rules; basic identities of trigonometric functions
including the summation angle and double angle formulas; special values of
trigonometric functions; derivatives of these functions

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**Calculator Skills:** Sketch graphs, tracing
intersection points and roots, finding numerical limits

**Miscellaneous Techniques: **quadratic formula for
roots, factorization of a^2-b^2, a^3-b^3, long
division; simplifying techniques: multiply and divide a same quantity, add and
subtract a same quantity to maintain and transform quantities

**Partial Review Problems**: All homework, quizzes,
lecture example problems, and sample exams