Hi,

Topic name: L'Hopital Rule

Please Have a thoughtful look through my answers to each question. If you found any mistake, please rewrite that question with the whole answer (Step By step). You can use the attached formulas for reference. please answer the questions in order.

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Types of Indeterminate forms . There are seven types of indeterminate forms : 1. 0/0 00 / DO In0 = 3 O X Do 00 - 90 CSux = 1 NOWAW Oo If y = sin(u) - y'=u'cos(u) Sinx 8 - If y = cos(u) - y'=-u'sin(u) secx = cost If y = tan(u) - y'=u'sec?(u) tanx = Sinx If y = cot(u) - y'=-u'csc2(u) GJX If y = sec(u) - y'=u'sec(u)tan(u) Colx = Cox Sinx If y = csc(u) - y'=-u'csc(u)cot(u)g) limx-o tan(x)In(x) = tan (o) In (0) = 0x0 X lim COS X * Sinx x - 0 sinx tanx Lost ( v = sinx cos (0 ) U : 1 V = cosX ( . ) cos ( 0 ) + sin ( o ) h) lim _n sec(3x) cos(5x)\fNAS NEA NEW ACADEMY SCHOOL Types of Indeterminate forms at, 1987 There are seven types of indeterminate forms : 0/0 2. 3. 00 / D O x Ino = 4. k) limx-0 xsinx 0 sin (0 ) 5. 0o CSUX = = 6. If y = sin(u) - y'su'cos(u) Sinx 1 = 1 7 If y = cos(u) - y'=-u'sin(u) Secx = Cost If y = tan(u) - y'=u'sec?(u) tank = Jinx lim sinic In 2 = sinGc ) In ( ox ) = In a If y = cot(u) - y'=-u'csc?(u) GIX If y = sec(u) - y'su'sec(u)tan(u) Colx = Cox since If y = csc(u) - y'=-u'csc(u)cot(u) Sinx sinx = sin (0 ) 1 O sinx (2 ) LOST X