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Sheet9 - Math 21A Kouba Challenge Discussion Sheet 9 1...

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Unformatted text preview: Math 21A Kouba Challenge Discussion Sheet 9 1.) Evaluate the following limits by using one of the three limit definitions for e. a.) ”11330 (1+3? b.) lim (1+3)" 0) lim (blfm n——)oo 7n n—> — oo 3n d-> .132. (23)" e-> in (1- g)” 2.) Solve for :13. a.) ln(2m+3)—ln(w+4) =0 b.) log(m)+log(m—21)=2 c.)e3“’+2-e“”=3-62” d.) e3x—3-ezm—2-em-l—620 3.) Solve f’(w) 2 0 and f”(m) = 0 for a: and set up a sign chart for each. a.) f(:L') = mlnrc. b.) f(:c) = ate—m2”. d 4.) Find y’ = 3%. Do not simplify your answers. 3-) y =1n[a:(m+ 1)(m+2)(w+3)(m+4)] b.) y z (a: + Desi” c.) 9095113 : 331% 5.) Consider the rectangle in the given sketch inscribed in the first quadrant below the graph of y = e('3/2)w. Determine the dimensions of the rectangle a.) with maximum area. b.) with minimum perimeter. c.) with minimum diagonal. Use Newton’s method to estimate the root of the deriva- tive equation to three decimal places. Y ...
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