Jawaban soal matematika

11. Nilai lim x = 0 , 1-√1+x/x^2-x =

Subtitusi :

=1-√1+0/0^2-0
=1-√1/-0
=1-1
=0

L'hopital :
= 1 /2. - √1+x /2x-1
= 1/2.-1 /2.0-1
= 1/-2/0-1
= 1/-2/-1
= 1/-2 x 1/-1
= 1/2

Jawabannya adalah c. 1/2

13. F(x) = 2x^3 -4x + 8
   F'(-1) = ....... ?
   F'(x) = 3.2x^2 - 4
         = 6x^2 - 4
  F'(-1) = 6.(-1)^2-4
         = 6.1 -4
         = 6 - 4
         = 2.

Jawabannya adalah c. 2

15. F(x) = 2x + 1 /√x - 3
   F'(4) = .....?

   u(x) = 2x + 1 » u'(x)  = 2
   v(x) = √x - 3 » v'(x)  = 1/2√x

h'(x) = u'(x) v(x) - u(x) v'(x) /(v(x))^2
     = 2.(√x -3) - (2x+1).(1/2√x) / (√x - 3)^2
     =(2)- (2x +1)(1/2√x) /(x-3)

h'(4) = 2(2√x) -(2x+1)/2√x/(√x-3)
      = 2(2√4) -2.4-1/2√4/(√4-3)
      = 2.4 - 8- 1/4/-1
      = 8-8-1/4/-1
      = -1/4/-1
      = -1/4 x 1/-1
      =  1/4

Jawabannya adalah d. 1/4

Sumber soal : Lks intan prawira mat kls 11 smt 2 hal 74