# Unit 4 Eric Yoseke .pdf - Unit 4 Extensions Instructions...

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Unit 4: Extensions Instructions There are 13 questions in this Assessment of Learning for a total of 79 possible 1. ?) lim 𝑥→0 cos ? ??????? ??? ?𝒂??? ? = ?, ?? ??? lim 𝑥→0 cos ? = cos(0) lim 𝑥→0 cos ? = 1 ??????? ?? ?ℎ? ????ℎ ? ??? ??? ?ℎ?? lim 𝑥→0 cos? = 1 ??? lim 𝑥→0 + cos? = 1, ???ℎ ????? ?? ?ℎ? ????? ??? ????? ??? ?ℎ?? ?? ?????????????. 𝑇ℎ??????? ?? ?? ????? ?ℎ?? lim 𝑥→0 cos? = 1 ?) lim 𝑥→∞ sin? ?????????? ????, lim 𝑛→∞ sin? , ? = 2?𝜋 lim 𝑛→∞ sin(2?𝜋 ) = 0 ??????? ? = (2? + 1 2 ) 𝜋 lim 𝑛→∞ sin((2? + 1 2 ) 𝜋) = 1 ?? lim 𝑛→∞ sin(?) ?? ????????? ?? ? → ∞ ∴ lim 𝑥→∞ sin? ???? ??? ?????. 2. ?) ? = sin? 5 ? = 𝐜? ?(? ? ) (?? ? ) ?)? = sin 5 ? ? = ?(?𝐢? ? ?) (????) ?) ? = cos(4? + 9) ? = − sin(4? + 9) (4) ? = −? ?𝐢?(?? + ?) ?) ? = cos 2 (? 2 + 3) ? = 2(cos(? 2 + 3))(− sin(? 2 + 3) (2?)) ? = −?????(? ? + ?)?𝐢?(? ? + ?)
?)? = ? 2 sin(? 2 + 5 ) ? = ? 2 (cos(? 2 + 5) (2?)) + sin(? 2 + 5) (2?) ? = ?? ? 𝐜??(? ? + ?) + ?????(? ? + ?) ?)? = 5? 𝑥 ? = ?? ? ?)? = ? 5𝑥 ? = ? 5𝑥 (5) ? = ?? ?? ℎ)? = ?? 3𝑥+1 ? = ?(? 3𝑥+1 (3)) + ? 3𝑥+1 (1) ? = 3?? 3𝑥+1 + ? 3𝑥+1 ? = ? ??+? (?? + ?) ?) ? = ln(? + 3) ? = ? ? + ? ?) ? = 5ln(? 2 + 4) ? = 5 ( 2? ? 2 + 4 ) + ln(? 2 + 4) (0) ? = ( ??? ? ? + ? ) ?) ? = 5 𝑥 ? = 5 𝑥 ln(5) ? = ?. ??(? ? ) ?)? = (? 2 + 2) 2 (? 2 + 2? + 1) 3 ? = (? 2 + 2) 2 (3(? 2 + 2? + 1) 2 (2? + 2)) + (? 2 + 2? + 1) 3 (2(? 2 + 2)(2?)) ? = 3(2? + 2)(? 2 + 2) 2 (? 2 + 2? + 1) 2 + 4?(? 2 + 2? + 1) 3 (? 2 + 2) ? = ?(? ? + ?)(? ? + ?? + ?) ? (?? ? + ?? ? + ?? + ?) ?) ? = ln(????) ? = ???? ???? ? = 𝐜??(?) ?) ? = (? + ???) 5 ? = 5(? + ???) 4 (1 + 1 ? ) ? = ?(? + ???) ? ( ? + ? ? )
3. ? = (? + 3) 2 (? + 2) 5 (? + 4) 7 ??? = ?? ( (𝑥+3) 2 (𝑥+2) 5 (𝑥+4) 7 ) ln ? = ln(? + 3) 2 − ln (? + 2) 5 − ln(? + 4) 7 1 ? ? = 2 ln(? + 3) − 5 ln(? + 2) − 7 ln(? + 4) 1 ? ? = 2 ( 1 ? + 3 ) − 5 ( 1 ? + 2 ) − 7 ( 1 ? + 4 ) ? = ? (( 2 ? + 3 ) − ( 5 ? + 2 ) − ( 7 ? + 4 )) ? = (? + 3) 2 (? + 2) 5 (? + 4) 7 (( 2 ? + 3 ) − ( 5 ? + 2 ) − ( 7 ? + 4 )) ? = (? + 3) 2 (? + 2) 5 (? + 4) 7 ( −10? 2 − 58? − 86 (? + 3)(? + 2)(? + 4) ) ? = −?(? + ?)(?? ? + ??? + ??) (? + ?) ? (? + ?) ? 4. ? = ln(? 2 − 2) , ? = 3 ? = 2? ? 2 − 2 ? = 3, ?