**Exam 1 Review Topics**

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**Basics: **concept of limit, left and right limit;
definition of continuity; removable and non-removable discontinuity; concept of
horizontal, vertical, oblique asymptotes; definition of derivative; tangent line,
secant line; concept of average and instantaneous slopes/velocities; concept
and 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; find limits of undetermined types: ∞/∞, 0/0; find limits by
Squeeze Theorem; find limits by power rules, linearity rule; find horizontal,
vertical, oblique asymptotes (using long division); find roots of polynomials
through factorization; finding derivative by definition; derivatives of
elementary functions including polynomials, 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; hand sketch lines, parabola, cubic functions, trigonometric functions,
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; basic identities of
trigonometric functions including summation angle, double angle, half 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