Math+19A+-+Review+1+-+Fall+11

# Math+19A+-+Review+1+-+Fall+11 - fgh(0 if f(0 = 1 f(0 =-3...

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Math 19A - Review 1 - Fall 11 1.) Find the value of c that makes f continuous at 2. f ( x ) = x 2 - 4 2 - x if x 6 = 2 c if x = 2 2.) Evaluate each limit. (a.) lim x 3 x 2 + 2 x - 15 x - 3 (b.) lim x 1 2 8 x 2 + 6 x - 5 6 x 2 - 17 x + 7 (c.) lim x →- 1 x 2 - 2 x - 3 3 x 4 + 2 x 3 + 5 x 2 + 7 x + 1 (d.) lim x →-∞ 5 x 6 + 3 x 2 + 2 6 x 3 - 7 x (e.) lim x →∞ ( 3 x - 9 x 2 + 2 x ) (f.) lim x 0 tan( x ) x (g.) lim x π 4 sin( x ) - cos( x ) cos(2 x ) (h.) lim x 0 1 - cos( x ) x 2

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(i.) lim x 0 ( 1 x 1 + x - 1 x ) (j.) lim x 0 1 - 4 x 3 x - 6 x (k.) lim x 2 6 - x - 2 3 - x - 1 3.) Use the definition of the derivative to differentiate each function. (a.) f ( x ) = x 3 - x + 1 (b.) g ( x ) = ax 2 + bx + c (c.) h ( x ) = x 2 + 1 (d.) F ( x ) = x - 2 3 x + 1 (e.) G ( x ) = x 2 x + 3 4.) Differentiate each function. (a.) f ( x ) = x 2 - 1 x 2 + 1 (b.) g ( x ) = tan( x ) x 5 (c.) h ( x ) = 3 x cos( x ) (d.) F ( x ) = sin( x ) - x cos( x ) + 1 (e.) G ( x ) = x 3 e x sec( x ) (f.) H ( x ) = x 2 1 - x 3 sin( x )
5.) Find an equation of the tangent line to the given curve at the specified point. (a.) y = x 5 + x 3 + x ; (1 , 3) (b.) y = x + x ; (1 , 2) 6.) Find the two points on the curve y = x 3 - x 2 - x +1 where the tangent is horizontal. 7.) Assume
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Unformatted text preview: fgh ) (0) if f (0) = 1 , f (0) =-3 , g (0) =-2 , g (0) =-1 , h (0) =-5, and h (0) = 2. 8.) Assuming f is a diﬀerentiable function, ﬁnd an expression for the derivative of each of the following functions: (a.) y = x 5 f ( x ) (b.) y = f ( x ) x 3 (c.) y = 1 + xf ( x ) x 2 9.) Find all points on the curve y = sin( x )cos( x ) where the tangent line is parallel to the line x + 2 y = 3. 10.) Where does the normal line to the parabola y = x-x 2 at the point (1 , 0) intersect the parabola a second time? 11.) Find equations of both lines through the point (2 ,-3) that are tangent to the parabola y = x 2 + x ....
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