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# discussion3 - Math 21A Kouba Discussion Sheet 3 1 Evaluate...

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Unformatted text preview: Math 21A Kouba Discussion Sheet 3 1.) Evaluate the following limits. . v5 +3: — 3 . a.) align; ﬂ— b.) \$1320 (x—mcos(4/a:)) 2 . c.)lim,—“’ (HINTzwgl.) x—+0 sma: — :13 IE 2.) Use one-sided limits and limits to inﬁnity to ﬁnd all vertical and horizontal asymptotes for the following functions. Use the asymptotes together with x— and y—intercepts to sketch graphs of each function. ‘ m—2 x+2 a.)y=x2_9 b')y=m2(m+l) 3 3.) Give an 6,6 -proof for 213111 lx++\/§ = 4.) Use the IMVT to determine if the following equation is solvable. This is a writing exercise: \$3+m—\/m+4=0. 2 . 5.) In the given diagram the smaller circle is the largest one that can be inscribed in the given semi-circle. If the larger circle has circumference 47r in., what is the area of the inscribed shaded square ? 6.) Determine the x-values for which the following function is continuous. It is not necessary to graph the function : 3‘13"”, if m < 0 3.01, if a: = 0 f(113) Z x — 1 if0<m<1 Q:__ A‘.-§ ._ 1’ ' 2, if :1: Z 1 . ‘ \\ 7.) Use the limit deﬁnition of derivative, L\\ "IIV . ﬂw+M—[email protected]) / _ f (x) - #3; h each of the following functions. , to differentiate a.) f(a:) : cosa: b.) Ax) = 3:"; c.) f(a:) = W62 + :1: 8.) Let f(x) Wm) {sin2x, ifx Z 0 . . Use the limit deﬁnition of derivative to determine 21:, if m < 0 . +++++++++++++++++++++++++++++++++++++++++++ The following problem is for recreational purposes only. 9.) Without lifting your pencil, join all sixteen dots with six straight lines. 0 I O t O O Q 0 o I 5 0 0 o O O ...
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discussion3 - Math 21A Kouba Discussion Sheet 3 1 Evaluate...

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