MATH111-200630-QZ01-Solutions

MATH111-200630-QZ01-Solutions - Math 111 Quiz 1 Solutions...

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Unformatted text preview: Math 111 Quiz 1 Solutions DRAFT Edward Doolittle September 27, 2006 1. First evaluate the indefinite integral. Let u Check by differentiating. Now evaluate the definite integral: 2. First, find the y-value of the point on the curve. When x0 y0 , 1 So the point on the curve is x0 y0 2 e 2 . Next find the slope of the tangent line through that point. By the product rule, the derivative of the function is So the derivative for the given value of x0 is That is the slope m of the tangent line. Since we know a point through which the line passes and the slope of the line, we can write down an equation in point-slope form y y0 m x x0 : The equation of the line can be put into another form if you so desire, but the answer is fine as it stands. 1 y 2 2 x y x0 0 1 e e 2 ! y 2 2 e 2 cos 2 e 2 sin 2 y ex cos x ex sin x e ex0 cos x0 e 2 sin 2 e 2 My calculator says that the value of the integral is approximately 1 1695 0 0 1020. e 2 e 2 xe3x dx 2 e3 0 2 4 1 3x2 e 6 4 1 3 42 e 6 1 48 e 6 1 e 2 C xe3x dx 2 eu du 6 1 u e 6 3x2 . Then du 6x dx and 1 3x2 e 6 C ...
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