2]

lim (x^2 - 3x + 2)/(x - 1)

x->3

= lim [(x - 2)(x - 1)/(x - 1)]

...x->3

= lim (x - 2)

..x->3

= 3 - 2

= 1 (C)

3]

y = (x + 3)(2x - 1)

f(x) = x + 3 => f'(x) = 1

g(x) = 2x - 1 => g'(x) = 2

dy/dx = f'(x).g(x) + f(x).g'(x)

dy/dx = 1(2x - 1) + (x + 3)(2)

dy/dx = 2x - 1 + 2x + 6

dy/dx = 4x + 5 (A)

4]

f(x) = (2x + 3)/(3x - 4) , x =/= 4/3

a = 2x + 3 => a' = 2

b = 3x - 4 => b' = 3

f'(x) = (a' . b - a . b')/(b)^2

f'(x) = [2(3x - 4) - (2x + 3)(3)]/(3x - 4)^2

f'(x) = (6x - 8 - 6x - 9)/(3x - 4)^2

f'(x) = -17/(3x - 4)^2 (C)

5]

f(x) = mx^3 + 2x - 1

f'(-1) = -1

f(x) = mx^3 + 2x - 1

f'(x) = 3mx^2 + 2

f'(-1) = 3m(-1)^2 + 2

f'(-1) = 3m(1) + 2

f'(-1) = 3m + 2

-1 = 3m + 2

3m = -1 - 2

3m = -3

m = -3/3

m = -1

f(x) = mx^3 + 2x - 1

f(x) = (-1)x^3 + 2x - 1

f(x) = -x^3 + 2x - 1

f(1) = -1^3 + 2(1) - 1

f(1) = -1 + 2 - 1

f(1) = 0 (C)

6]

f(x) = 1/2 x^2 - 8x + 3

f'(x) = x - 8

f'(2) = 2 - 8

f'(2) = -6 (A)