Explain with leasons why limxrarr-2nbsp fx exists but fx is

Question

Question 1:

            -2x +1                    x <  -2

 f(x) =    x² + 1        if        -2 < x < 1

            2x                          1 ≤ x ≤ 3

            5                            x ≥ 3

1.1 Explain with leasons why lim_x→-2  f(x) exists, but f(x) is not continuos at x = -2. State the type of discontinuity.

1.2 What type of discontinuity exists at x = 3 ?

1.3 Show that f(x) is continuous and diffrent table at x = 1.

1.4 For what value(s) of x is f'(x) = 0

1.5 If g(x) = √2x, determine the value of (gof)(-1)

1.6 If h(x) = 3x², determine h(g(x)).

Question 2:

2.1 Determine f'(x) from first principles if f(x) = 5/x-2

2.2 differntiate with respect to x:

2.2.1 Dx[√3x⁵ - 2x⁴]

2.2.2 f'(x) if f(x) = 5x³(2x + 1)¹²