2024 2nd sem Calculus revision

• Integration by parts

• Integration by parts

In order to prove that f(x) is continuous at x=a we need to check (choose all that applies)

• f(a) is well-defined

If we know that f is 2 times differentiable then
(choose all)

• f is continuous

• f' is continuous

• f'' is continuous

• f''' is continuous

Does the function satisfy conditions of the EVT on [0.5 ; 2.5]

• Yes

• No, no continuity

• No, no differentiability

• No, because of the interval

The graph of the function f is shown. At what one point on the graph are the following statements true? f(x)>0,   f′(x)<0   and   f′′(x)<0

• M

• N

• P

• Q

• R

It follows from IVT that there is a∈[-1;1] : f(a)=0

• TRUE because there is a sign change on the interval

• FALSE because there is no sign change on the interval

• FALSE because the function is discontinuous on the interval

• FALSE because the function is not differentiable on the interval

• 1

• 0

• doesn't exist

The function f is continuous on the closed interval [1, 5] and differentiable on (1,5). The table below gives selected values of f on this interval. Which of the following statements must be TRUE?

• The minimum value of f on [1, 5] must be -2