# Disc7 - Math 21A Kouba Discussion Sheet 7 1 Find the slope...

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Unformatted text preview: Math 21A Kouba Discussion Sheet 7 1.) Find the slope and concavity of the graph of mgr/2 + y = 2 at a: = 0 and at x = 1 . Sketch the graph of this equation. 2.) Evaluate the following limits by using one of the three limit deﬁnitions for e. a.) hm (1+E)n b_) hm (1_§)n c.) lim (1+—1-)4n n—boo n n—mo n n—r—oo 5n d.) lim (n+4)_n e.) lim ( n )2" f.) lim (1+3h)2/h n—~)oo n, n—>—oo h—>0 3.) Solve for ac. a.) lncc=3 b.) lnm=ln3 c.) ln(2m+1)—ln(\$+3) =0 d.) ln(;v — 1) + ln(:v — 2) = 0 e.) 1n(:1: — 2) + ln(:I: + 2) — lnm = 1n3 4.) Let f(a:) = 3:3 lnm. Solve f’(a:) = 0 and f”(x) = O for a: and set up a Sign chart for each. d 5.) Find 31’ = d—Z as simply as possible. Do not simplify your answers. as + 1)5 -cos(2x) -tan10x d.) y = 331‘” e.) y = \$3 - (m —— 1:35 - (2:17 + 3)7 - (3m — 4)9 - (4:8 + 5)11 a.) y = ln(5m+7) b.) y = ln(ln(ln(sin:c))) c.) y = 1n sin 2:) 2 . f-) y = (2\$)\$+3 g-) y : my h-) 9 = \$(y 1-) y :10g5(10g4(10g3 6.) Solve for :L'. a.) e“c = 2 b.) 7 - e2x+3 = 63—“: c.) (ex +1)(e”‘ — 5) = 0 d.) e2z—4-e”=0 e.)e2\$——5-e“+6=0 . d . . 7.) Flnd y’ = d—y . Do not Simplify your answers. :3 2373+4Cc 1:5 a. =7-5m_4 b. =\$2-t 3 . = d = 3 )3; e )1; e am) c>y 3H5. >11 4 8.) Find all horizontal asymptotes for the function in 7.)c.). 9.) Let f(\$) = x2 - e‘“. Solve f’(\$) : 0 and f”(ac) = 0 for a: and set up a sign chart for each. d d2 . 10.) Find d—y and 3—3:— when t = 1 for each set of parametric equations. 33 :1: m=ﬁ+t a.) 2 y=t —t, f0r0_<_t<oo. b) z=sint ' yzcos2t, forOﬁtSZvr. 1 1.) Differentiate. a_) y = arctan(3x) b.) y 2 at; - arcsin(ezm) c.) y = arccos(sin \$2) arccos w — arctan x d. = 0082 arctanx 3 e. :: .___—_—__— ) y ) ) ) y arctana: — arcsinx 53—1 f.) y = arcsin ( ) + 2 arctan (Simplify answer.) z+1 +++++++++++++++++++++++++++++++ The following problem is for recreational purposes only. 12.) Find a. hidden pattern and determine the next number in the sequence : 0,1,3,7,14,25,41,63,.. . ...
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Disc7 - Math 21A Kouba Discussion Sheet 7 1 Find the slope...

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