When f, g, F and G are functions such that lim f(x) = 0, lim g(x) = 0, lim F(x) = 2, lim G(x) = ∞, III which, if any, of A. lim f(x)g(x), B. lim f(x)9(2), 2+1 g(x) 1+1 G(T)* are indeterminate forms? C. lim 1. A and C only 2. B only 3. C only 4. A only 5. B and C only 6. all of them 7. none of them 8. A and B only

Q: 4. /xln2xdx хрх

A:

Q: Find the index of 12Z in 3Z

A: The integers are

Q: Using Euler's Theorem, Find the last two digits of 123402

A:

Q: If permutaiton A=(123)(145), then A2=?

A:

Q: Use Euler's theorem to Find the last two digits of 172002

A:

Q: to

A:

Q: 14 nC AU Conc=

A: Defination: n(A∪B)=n(A)+n(B)-n(A∩B) n(A∩B): common area of A and B n(A∩B∩C):Common area of A,B and C

Q: 1. In x x² dx

A: The given integral is: I=∫16lnxx2dx   So, we can also write as; ∫16lnxx2dx=∫16lnx·1x2dx=∫16lnx·x-2dx…

Q: 5. Show that () = () +().

A:

Q: Fill in the blanks identified by ‘*’ and ‘**’.

A: The given output is obtained from the MINITAB software.

Q: (- 1)" _ 3 En=0 'n =D0 3" 4 Select one: True O False

A:

Q: 6. (a) Find the units digit of 3100 by the use of Fermat's theorem.

A: We need to find the last digit ,therefore find 3100≡xmod 10 According to Fermat's little theorem…

Q: Find, with justification, the last digit of 8^8^8^8.

A: The given question is solved below.

Q: -1 1 x+1 coth - In X = 2 x-1

A: We have to prove coth-1x=12lnx+1x-1

Q: 4.) T(:) = + 2x-] relate to the baseB, = {H(},and B,,

A:

Q: 8. [ tan’rd.r

A: We have to find the integration of given questions.

Q: 18. Find Itm,..(xe -x) O 2 O O O

A:

Q: осод ва меньва оз 4.th order. вида у со.в), comest Фу decimal placesi 16 - д-х2, у (06) =117379

A: Disclaimer: Since you have asked multiple questions, we will solve the first question for you. If…

Q: In 3 - In x - In(x + 5) = 0

A:

Q: for a -1 2x +5 f (x) = If fis the function defined above, then f' (-1) is A -2 B 3. E) nonexistent…

A:

Q: .Findthefirst4termsineachsequences a) tn=3(-2)^n-1

A: Find the first four term

Q: [0,342 -0,93 -0,2581] -0,93 -0,342 0,965 5,2 0 0 x = ?y=? z=? JE]- 105,3 -284,49 -1255,8]

A: The given system is:.If the given system is: , then the augmented matrix is given by:.So, the…

Q: let s be positive integer, then (2) + (;) = %3D

A: sC5 = s!/5!*(s-5!) And sC6 = s!/6!*(s-6)!

Q: (6!)! (3!)! = x! x = ?

A: Formula:

Q: dx (1)(- 2e * )

A:

Q: 31. In(1+ /2)

A: We have to convert ln1+2 into complex number.

Q: Represent the number 1080719 in sexagesimal notation.

A:

Q: Approximate the value of In (1000!)

A: Given that ln1000!. The objective is to approximate the value. The expansion for…

Q: Fad the inverse f AB f 4. 5. and -1 AU

A: Given that , A-1=5-11-5 and B-1=-3-31-1 find inverse of AB.

Q: 12. Let the "Fibonacci-2" numbers g, be defined as follows: 91 = 2, 92 = 2, and gn+2 =( In+1)( In)…

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Q: Using Euler’s Theorem, find the last two digits of 4444^3333

A: Let us find the last two digit of the given expression by using Euler's Theorem in the next steps.