Quiz in class

What is a function in calculus?

• A relation that assigns each element from one set to exactly one element from another set

• A mathematical expression that has no variables

• A type of equation that cannot be solved

• A graphical representation of data

What does it mean for a function to be continuous at a point?

• The function is defined at that point

• The function has a limit at that point

• The increment of the function over small intervals is small

• The function has a derivative at that point

What is the Mean Value Theorem?

• A theorem that states a function must be continuous to have a derivative

• A theorem that guarantees a point where the derivative equals the average rate of change

• A theorem that applies only to polynomial functions

• A theorem that states all functions are differentiable

What is a differentiable function?

• A function that has no limits

• A function that has a derivative at every point in its domain

• A function that is continuous everywhere

• A function that is defined only on integers

What is a left-continuous function?

• A function that approaches a limit from the left

• A function that is continuous at every point

• A function that has a limit from the right

• A function that is defined only for negative values

What is the definition of a jump discontinuity?

• A point where the function has a derivative

• A point where both limits exist but are not equal

• A point where the function is not defined

• A point where the function is continuous

What is a C1 function?

• A function that is discontinuous everywhere

• A function that is only defined at one point

• A function that is continuous and has a continuous derivative

• A function that has no derivatives

What is a càdlàg function?

• A function that is continuous from the left and right

• A function that is only defined for positive values

• A function that is right-continuous with left limits

• A function that has no limits

What is the primary focus of stochastic calculus?

• To find the maximum of continuous functions

• To solve polynomial equations

• To analyze random processes and their properties

• To study functions with discontinuities of the second kind

What does the notation △g(t) typically represent in standard calculus?

• The increment of g over a specified interval

• The derivative of g

• The area under the curve of g

• The limit of g as t approaches zero