Find the volume by Cylindrical shells - Find the volume of revolution you obtain by rotating about the $x$-axis the area enclosed by the curve $y=e^x$, $y=1$, $x=1$.

QUESTION: Find the volume of revolution you obtain by rotating about the $x$-axis the area enclosed by the curve $y=e^x$, $y=1$, $x=1$.


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PROBLEM: Why should the graphs of $f(x,y)=x^2+y^2$ and $g(x,y)=-x^2-y^2+xy^3$ be called 'tangent' at $(0,0)$?

PROBLEM: Why should the graphs of $f(x,y)=x^2+y^2$ and $g(x,y)=-x^2-y^2+xy^3$ be called 'tangent' at $(0,0)$?

travel Graphs, speed, distance, time. Shown are graphs of the position function of two runners, A and B, who run a 100-m race and finish in a tie. a) Describe and compare how the runners run the race. b) At what time is the distance between the runners the greatest? c) At what time do they have the same velocity?

QUESTION
Shown are graphs of the position function of two runners, A and B, who run a 100-m race and finish in a tie. 
a) Describe and compare how the runners run the race. 
b) At what time is the distance between the runners the greatest? 
c) At what time do they have the same velocity?