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Exam 2 Study Guide for Math 127

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by: Monica Weisenbach

Exam 2 Study Guide for Math 127 MATH127

Marketplace > University of Massachusetts > Mathematics (M) > MATH127 > Exam 2 Study Guide for Math 127
Monica Weisenbach
GPA 3.819
Calculus I for Life and Social Science Majors
Thurlow Cook

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About this Document

This is a study guide for the second exam of the semester for Calculus 127. It contains a quick review of important formulas and concepts, as well as stuff learned more recently (up to 4/1/15). Any...
Calculus I for Life and Social Science Majors
Thurlow Cook
Study Guide
Umass Amherst, Math, Calculus, math 127
50 ?




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1 review
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"Clutch. So clutch. Thank you sooo much Monica!!! Thanks so much for your help! Needed it bad lol"
Issac Larson Sr.

Popular in Calculus I for Life and Social Science Majors

Popular in Mathematics (M)

This 6 page Study Guide was uploaded by Monica Weisenbach on Thursday April 2, 2015. The Study Guide belongs to MATH127 at University of Massachusetts taught by Thurlow Cook in Spring2015. Since its upload, it has received 158 views. For similar materials see Calculus I for Life and Social Science Majors in Mathematics (M) at University of Massachusetts.

Similar to MATH127 at UMass


Reviews for Exam 2 Study Guide for Math 127

Star Star Star Star Star

Clutch. So clutch. Thank you sooo much Monica!!! Thanks so much for your help! Needed it bad lol

-Issac Larson Sr.


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Date Created: 04/02/15
Exam Study Guide Stuff to Remember Just in case fX gX fgX f gX fX gX fgx input x into g take that new value place into f gfx input x into f take that new value place into g Equations of lines ymxb linear yyomxxo pointslope yax2bxc quadratic Quadratic Formula x b xb24ac2a SOHCAHTOA For sine function asinbx a is the amplitude 2nb is the period LogabX xlogab Logabc logab logac Logabc logab logac X Xquot12 Rate of change fx fXoXXo lim fxh fx f x hgtgtO h What are the derivatives The derivative is the slope of the line at a point For linear lines the slope is the same For nonlinear lines the slope changes at each point Technically the derivative is the slope of the tangent line at said point f x dydx ddx all ways to write the derivative List of Derivatives Power functions xn nxn1 Exponential functions nX nXnn Sine functions sinx cosx Cosine functions cosx sinx Natural logarithm functions lnx 1x eX eX ekx kekx Number n O The Manipulation of Derivatives Manipulations fg X f X 9 X af X af X Product rule fg f g fg Quotient rule fg f g fg g2 Chain rule AB where B is a function acting on A ddx A ddx B Concept Question Answer derivative Power 3x2 6x Exponential 7X 7 Natural log ln8x 18x Chain rule 5ln1e 5e Product rule xeX eX Chain rule ln2x 10ln2x Quotient rule lnxx 1 lnxx First derivative the derivative of the original equation The zeroes of this equation equate to minimums and maximums on the graph Positive graph is increasing negative graph is decreasing O maximum O minimum Second derivative the derivative of the first derivative The zeroes of this equation equate to points of inflection on the graph Positive concave up negative concave down O and O changes in the value of the second derivative show that the graph is changing shape in it s curve 0 Max5 mln 0 0 o Revenue Functions Revenue pricequantity Marginal revenue derivative of revenue equation Cost cost of producing itemquantity initial fixed cost Marginal cost derivative of cost function Profit revenue cost Profit is maximized when R 0 when marginal revenue and cost is equal If 0 Cql pro l P flit Ir cap gt Roi loSS crash0 c Logistic Growth Curve The equation is L1Ceki L limit k is the growth rate L i L2 is the inflection point for the curve 7392 1quot quotquotrquot The greatest rate of change is at the inflection point Integral The integral is the area under the graph shown by the symbol f It s units are the units of y times the units of x It can be estimated with lower and upper estimates using rectangles I I 1 l a 1in quot 1 To find an estimate of the integral between 1 and 2 on this graph find the values x 1 54 32 74 2 y 1 45 8 23 67 47 59 12 5 The lower estimate uses the left hand points of the rectangles In this case it s 14186759 The right estimate uses the right hand points of the rectangles In this case it s 14867592 Add those up find the average divide by 2 and you have a Close estimate Another way to remember this is that both upperlower estimates have the same number of terms as there are intervals the above example has 4 intervals so 4 terms per estimate and the lower starts on the lowest value while the upper ends on the highest value Definite Integral is fab fXdX a is the lower xvalue b is the xvalue dx is the size of the interval The area between two curves is fab fXgxdx A fab fXgxdx where fX 12x and gx x A fab 12xxdx fab 1xdx These notes only go up to 41 this does not include notes from 42 A section on integrals will be probably released next week


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