# For all parts in question #1 f x = e ° 2 x a Write the...

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MAT 131-Final Exam-Fall 2014 NAME:_____________________________ TA NAME:_____________________________ ° Each numbered question is worth 20 points. 1. For all parts in question #1 f ( x ) = e ° 2 x a.) Write the equation of the tangent line to f at x=1. b) Write an expression in sigma notation that represents the area under f from x = 0 to x = 1 : 1
c) Find the exact value of the area under f from x = 0 to x = 1 : d) Sketch a graph of f 0 . 2
2. Draw y = F ( x ) = R x 1 ( ± 1 + j t + 2 j ) dt with correct concavity on a scaled set of axes. (Include at least 3 labeled points.) 3
3. Use a left Riemann estimate with 2 subintervals to approximate the area between dy dx = p x 3 + 1 and the x axis from x = ± 1 to x = 5 . Now use this value to sketch y = f ( x ) if f ( ± 1) = 2 4
4 ) Determine the following limits or explain why they do not exist if f ( x ) = ln j x j x a ) lim x ! 0 f ( x ) b ) lim x !°1 f ( x ) c ) lim x ! e ln( f ( x )) 5
5 : Evaluate: a) R (99 cos x ± 2) dx b) R 3 p 5 x ± 9 dx 6
c ) R 9 1+ x 2 dx d ) R e x tan( e x ) dx 7