Limits Continuity

Let f(x) = 4 and f′(x) = 4

Let f(x) = 4 and f′(x) = 4. Then Lim_x→2 (xf(2) - 2f(x))/(x-2) is given by

1. -4
2. 2
3. -2
4. 3

If f: R → R is a function defined by f(x) = [x] cos((2x - 1)/2)π

If f: R → R is a function defined by f(x) = [x] cos((2x - 1)/2)π, where [x] denotes the greatest integer function, then f is

1. discontinuous only at x = 0
2. discontinuous only at non-zero integral values of x
3. continuous only at x = 0
4. continuous for every real x

The value of p and q for which the function

The value of p and q for which the function

f(x) = (sin(p + 1)x + sinx)/x, x < 0
f(x) = q, x = 0
f(x) = (√(x + x²) - √x)/x^3/2, x > 0

is continuous for all x in R, are:

1. p = 1/2 , q = 3/2
2. p = -3/2 , q = 1/2
3. p = 1/2 , q = -3/2
4. p = 5/2 , q = 1/2

Let f(x) = 4 and f′(x) = 4. Then Limx→2 (x f(2) − 2 f(x)) / (x − 2) is given by

Let f(x) = 4 and f′(x) = 4. Then Lim_x→2 (x f(2) − 2 f(x)) / (x − 2) is given by

1. -4
2. 2
3. 3
4. -2