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Unformatted text preview: Review for MA 141: (THIS IS NOT ALL INCLUSIVE) What is the theorem that relates one sided limits with regular limits? Specifically, if you know lim x a f ( x ) = L , then what can you say about lim x a + f ( x ) and lim x a f ( x )? If you know lim x a + f ( x ) = L = lim x a f ( x ), then what can you say about lim x a f ( x )? (2.3, Q: 32, 35) There are 11 important limit laws. What are they? (2.3, Q:1,2, 11, 13, 15, 16, 19) What is the definition of continuity? Specifically, what does it mean for a function f ( x ) to be continuous at x = a ? What are the 4 (possibly 2, depending on your perspective) values that you can check to determine continuity? That is, there are 4 values that need to be equal for a function f ( x ) to be continuous at x = a . If these values are equal, the function is continuous at x = a . If these values are not all equal, then the function is not continuous at x = a . (2.4, Q: 10, 11, 14, 15) What is the definition of the derivative (see text, section 2.8)? What information does the derivative give you? How can you find the slope of a tangent line? How do you write the equation of a tangent line to a curve at a given point? What is the signifi cance of the tangent line? ( { 2.6, Q: 10, 18 } ; { 2.7, Q: 9, 25, 26 } ; { 2.8, Q: 22, 23, 31, 34 } ) If an object is moving along a straight line with position given by s ( t ), where t is time, what do s ( t ) and s 00 ( t ) represent? What does the derivative, f ( x ) tell you about the function f ( x )? What does the sec ond derivative, f 00 ( x ), tell you about the function f ( x )? (2.9, Q: 11, 23, 24) The derivative of a constant function is always...? The power rule for differentiation is...? The sum/difference rule for differentiation is...? The derivative of e x (w.r.t. x ) is...? The product for differentiation says...? The quotient rule for differentiation says...?(3.1, 3.2, Table on page 198). ( { 3.1, Q: 127, 41, 42, 48 } ; { 3.2, Q: 312, 2124, 31, 37 } ) The derivative of f ( x ) = sin ( x ) is...? The derivative of f ( x ) = cos ( x ) is...? The derivative of f ( x ) = tan ( x ) is...? 1 (3.4, Q: 115, 17, 18, 27) The chain rule allows us to differentiate fill in the blank functions. The chain rule says...? (3.5, Q: 7, 8, 11, 16, 19, 25, 28) Implicit differentiation. y is assumed to be a function of x , but you cannot solve for y in terms of x (i.e., you cant write y = an expression of x alone), so you differen tiate the equation implicitly to find dy dx . As opposed to normal differentiation, dy dx now depends on both the...
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 Fall '07
 WEARS
 Limits

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