Continuity and Differentiability

1A function f is continuous at x = a if:

• Alim_{x→a} f(x) = f(a) (and both exist)
• Bf(a) is defined only
• Clim_{x→a} f(x) exists only
• Df is differentiable at a

2The derivative of sin x with respect to x is:

• Acos x
• B−cos x
• C−sin x
• Dtan x

3If f(x) = e^(2x), then f'(x) is:

• Ae^(2x)
• B2e^(2x)
• C2x e^(2x)
• De^x

4Differentiability implies:

• AContinuity, but not conversely
• BContinuity, and conversely
• CNeither implies the other
• DContinuity at all points except corners

5The derivative of x^n (where n is a real number) is:

• An · x^(n−1)
• Bn · x^n
• Cx^(n−1)
• Dn^(x−1)