MATH1271 Midterm 1 Exam Analysis

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MATH 1271
Scot Adams

Priyanka Ketkar Exam Analysis Calculus I Midterm 1 Test Breakdown The main topics covered in Midterm 1 were limits rate of change continuity function domains logarithms functions and differentiabilityThe test usually has 1415 questionsPart I There are 6 multiple choice questions with 5 choices The questions mainly deal with limits or rate of changePart II There are 5 True or False questions They are usually simple and generally have direct reference to certain properties of functions These questions mainly deal with limits continuity function domains and differentiabilityPart III There are 3 or 4 free response questions and some have multiple parts These questions require more indepth knowledge and higherlevel problem solving skills These questions mainly deal with limits rate of change and functionsTest Statistics Topics Spring 2011 Fall 2011 Spring 2012 Spring 2013 Total Limits 8 8 6 7 29 Rate of Change 3 1 48 Continuity 3 12 4 Function 2 1 1 3 7 Domains Logarithms1 12 Functions1 2 2 5 Differentiability1 23Topic 1 Limits 1 Knowledge Summary The limit of a function is the value the function approaches as x approaches a certain value The expression refers to the limit as x approaches a from the right The expression refers to the limit as x approaches a from the left The expression The expression refers to the limit as x approaches a from bothsidesA horizontal asymptote of a function is also the limit of that function to eitherorProperties 1 Sum and difference The limit of a sumdifference of two functions is the sumdifference of the limits of the separate functions 2 Product or quotient The limit of a productquotient of two functions is the productquotient of the limits of the separate functions as long as the denominator is not 0 for quotientsor3 Exponents The limit of a rational power of a function is the power of the limit of the function the exponent should not be 0 and the limit should be a real number TRIGONOMETRIC LIMITS o sinx0 x0o cosx1 x0o tanx0 x0o cscxDNE x0secx1 x0o cotxDNE x0osinax1 x0 ax1cosax0 x0 ax INDETERMINATES An indeterminate occurs when two laws of mathematics conflict when evaluating a limit for example001 etc Basically it means do more work A finite indeterminate occurs when x approaches a finite number There are 2 options for this case 1 Factor the function cancel any like factors and reevaluate the limit 2 Graph the function and visually inspect what value the function approaches from the left and right
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