MATH 273.001 Spring 2025: Exam 2 Review

These flashcards cover key concepts, theorems, formulas, and essential skills for Exam 2 in MATH 273.001.

The interpretations of the derivative include the definition at a point and as a function, denoted as and .

f′(x) and the Leibniz notation df/dx.

The equation of a tangent line to a graph can be derived using the concept of __.

derivatives.

The chain rule is a rule in differentiation that can be found in section __.

3.6.

The formulas for the derivatives of trigonometric functions, such as sin(x) and cos(x), can be found in section __.

3.5.

To evaluate if a function is differentiable at a point, one must consider the function's __ and its graph.

formula.

Logarithmic differentiation is a technique covered in section __.

3.9.

The __ is calculated by determining the slope at a specific point on the function's graph or tangent line.

tangent line.

The expression for the distance of a particle moving along a horizontal line after t seconds is given by __.

s(t) = √(4 + 9t²).

To find the rate at which the area of a rectangle is changing when the length is 20 inches and the width is 18 inches, one must consider the rates of change of both and .

length and width.

The values of two differentiable functions can be defined through expressions such as and .

u(x) = e^(2x)f(x), v(x) = tan(g(x)).

A particle's velocity and acceleration are functions evaluated from the particle's __ as a function of time.

distance.

The instantaneous rate of change of y = √(1 + x³) at the point (2, 3) can be determined through __.

the derivative.

The relationship between the increasing height of a balloon and a boy's distance from the ground can be modeled using __.

related rates.

Implicit differentiation allows solving for __ without explicitly solving for y.

dy/dx.