34 Questions
What is the definition of derivative for a function f(x)?
The sensitivity to change of the function value with respect to a change in its argument.
How can differentiation be defined in the field of calculus?
Differentiation enables us to determine how one quantity changes with regard to another.
What does the derivative of a function represent at any point within its domain?
The slope of the function at that point.
Under what condition are functions differentiable?
Functions are differentiable only if they are continuous.
How can velocity be defined using the concept of derivative?
Velocity can be defined as the derivative of distance with respect to time.
What is the method to define the derivative of y = f(x) using the first principles?
The derivative of y = f(x) is defined by the limit of the change in y due to the change in x.
What is the main law used to find the derivative in the given text?
The definition of the derivative
What are the main steps involved in applying the law to find the derivative?
Write the law, find each part, simplify the value, and substitute in and evaluate the limit
In the context of finding the derivative, what does y / = lim Δx→0 f(x + Δx) − f(x) / Δx represent?
The definition of the derivative
What is the derivative of f(x) = 3?
0
What is the derivative of f(x) = 2x + 3?
2
What is the derivative of f(x) = x^2?
2x
What is the derivative of f(x) = x?
1
What is the derivative of f(x) = sin(2x)?
2cos(2x)
What law is used to simplify sin(2(x + Δx)) in the process of finding the derivative?
The addition sine law
What is the derivative of f(x) = cos(2x)?
-2sin(2x)
What is the derivative of f(x) = a*x?
a
What does the expression f(x + Δx) − f(x) / Δx represent in the context of finding the derivative?
The difference quotient
What percentage of the volume of concrete do aggregates occupy?
75%
What are the primary materials used as aggregates?
Sand, gravel, crushed stone
What must all aggregates be essentially free of?
Silt and/or organic matter
Name three types of coarse aggregates mentioned in the text.
Basalt, Dolomite, Gravel
What is the main purpose of providing concrete with coarse aggregates?
To resist the action of applied loads and show better durability
Apart from providing strength and durability, what other function do coarse aggregates serve in concrete?
To provide a relatively cheap filler
What are the fresh concrete properties affected by the aggregate content?
Workability, Consistency, Bleeding, Pumpability
What properties of hardened concrete are influenced by the aggregate percentage?
Strength, Modulus of Elasticity, Shrinkage, Abrasion, Durability
What is the significance of the nonlinearity relationship in concrete?
Formation of microcracks
What are the classifications of aggregates based on their source?
Natural, Artificial, Recycled
How are aggregates classified based on their size?
Fine Aggregates (d ≤ 4.75 mm), Coarse Aggregates (d > 4.75 mm)
What are the negative effects of flaky and elongated aggregate shapes on concrete?
Reduction in workability and durability
How does the surface texture of aggregate affect concrete?
Rough texture decreases workability but increases bond with cement paste
What are the different classifications of aggregates based on unit weight?
Normal weight, Light weight, Heavy weight
What is the unit weight range for normal-weight concrete produced using normal-weight aggregate?
2200 to 2400 kg/m3, 135-150 lb./ft3
What are the types of aggregates classified based on unit weight?
Normal weight, Light weight, Heavy weight
Learn about the definition of derivative and main derivative formulas in this chapter. Understand the sensitivity to change of a function value with respect to a change in its argument.
Make Your Own Quizzes and Flashcards
Convert your notes into interactive study material.
Get started for free
