lecture notes 1

lecture notes 1 - Review of Differentiation and...

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Review of DiFerentiation and Anti-diFerentiation As we begin Calculus II it is assumed that the student has covered the derivative of a function in some detail and has learned how to Fnd the anti-derivative of basic functions. This section is provided as a summary of some of these topics. Knowledge of trigonometric functions, exponential functions, and logarithmic functions is assumed, but will be reviewed as necessary throughout the course for reinforcement. Defnition oF derivative . Suppose f is deFned on an open interval containing x . The derivative of f at x is deFned by D x ( f ( x )) = f 0 ( x ) lim h 0 f ( x + h ) f ( x ) h Tangent line .I f f ( x 0 )= y 0 and f 0 ( x 0 m , then an equation for the line tangent to the curve y = f ( x ) is given by y y 0 = m ( x x 0 ) Rules of DiFerentiation Assume that a and b are real numbers and that f ( x ) and g ( x ) are di±erentiable on an open interval containing x . Rule 1. The derivative is linear. That is, D x ( af ( x )+ bg ( x ) ) = aD x ( f ( x )) + bD x ( g ( x )) = af 0 ( x bg 0 ( x ).
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lecture notes 1 - Review of Differentiation and...

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