Limits and continuity

1003164304

Level: 
C
Which of the following situations could arise for suitable functions f and g?
limx→2f(x)=∞ ∧ limx→2g(x)=−∞ ∧ limx→2[f(x)+g(x)]=−∞
limx→2f(x)=13 ∧ limx→2g(x)=0 ∧ limx→2f(x)g(x)=13
limx→2f(x)=−∞ ∧ limx→2g(x)=∞ ∧ limx→2[f(x)−g(x)]=0
limx→2f(x)=∞ ∧ limx→2g(x)=−∞ ∧ limx→2[f(x)⋅g(x)]=∞

1003164303

Level: 
C
Which of the following situations could arise for suitable functions f and g?
limx→5f(x)=0 ∧ limx→5g(x)=∞ ∧ limx→5[f(x)⋅g(x)]=13
limx→5f(x)=1 ∧ limx→5g(x)=∞ ∧ limx→5[f(x)⋅g(x)]=13
limx→5f(x)=∞ ∧ limx→5g(x)=∞ ∧ limx→5[f(x)⋅g(x)]=13
limx→5f(x)=−∞ ∧ limx→5g(x)=∞ ∧ limx→5[f(x)⋅g(x)]=13

1003164302

Level: 
C
Which of the following situations could arise for suitable functions f and g?
limx→2⁡f(x)=∞ ∧ limx→2g(x)=∞ ∧ limx→2[f(x)−g(x)]=∞
limx→2⁡f(x)=1 ∧ limx→2g(x)=∞ ∧ limx→2f(x)g(x)=1
limx→2⁡f(x)=−∞ ∧ limx→2g(x)=1 ∧ limx→2[f(x)+g(x)]=1
limx→2⁡f(x)=−∞ ∧ limx→2g(x)=−∞ ∧ limx→2[f(x)⋅g(x)]=−∞

1003164301

Level: 
C
Which of the following situations could arise for suitable functions f and g?
limx→3f(x)=∞ ∧ limx→3g(x)=∞ ∧ limx→3f(x)g(x)=5
limx→3f(x)=1 ∧ limx→3g(x)=∞ ∧ limx→3f(x)g(x)=5
limx→3f(x)=∞ ∧ limx→3g(x)=1 ∧ limx→3f(x)g(x)=5
limx→3f(x)=0 ∧ limx→3g(x)=∞ ∧ limx→3f(x)g(x)=5