COMPUTING LIMITS ALGEBRAICALLY
No calculator is allowed. Evaluate each limit algebraically.
Problem 1 :
Solution:
Problem 2 :
Solution:
Problem 3 :
Solution:
Problem 4 :
Solution:
Problem 5 :
Solution:
Problem 6 :
Solution:
Problem 7 :
Solution:
Problem 8 :
x→2x2+2x-8x-2
Solution:
=x→2x2+2x-8x-2=x→2(x-2)(x+4)(x-2)=x→2(x+4)=2+4=6
Problem 9 :
x→42x2-5x-12x-4
Solution:
=x→42x2-5x-12x-4=x→4(2x+3)(x-4)(x-4)=x→4(2x+3)=2(4)+3=11
Problem 10 :
x→-5x+5x3+125
Solution:
=x→-5x+5x3+125=x→-5x+5x3+53a3+b3=(a+b)a2+b2-ab=x→-5(x+5)(x+5)x2-5x+25=x→-51x2-5x+25=1(-5)2-5(-5)+25=175
Problem 11 :
x→3x3-3x2-4x+12x-3
Solution:
=x→3x3-3x2-4x+12x-3=x→3x3-3x2-(4x-12)(x-3)=x→3x2(x-3)-4(x-3)(x-3)=x→3x2-4(x-3)(x-3)=x→3x2-4=32-4=9-4=5