The document discusses explicit and implicit functions. An explicit function expresses the dependent variable in terms of the independent variable, while an implicit function does not. Implicit differentiation is used when the variables in an applied problem are related through an implicit formula rather than an explicit one. The process of implicit differentiation involves taking the derivative of both sides of the implicit equation with respect to the independent variable and solving for the derivative of the dependent variable. The total derivative describes the derivative of a function that depends on variables that are themselves functions of other variables, and can be calculated using a chain rule formula involving the partial derivatives.
Application of definite integrals,we will explore some of the many application of definite integral by using it to calculate areas between two curves, volumes, length of curves, and several other application.
In mathematics, a partial derivative of a function of several variables is its derivative with respect to one of those variables, with the others held constant (as opposed to the total derivative, in which all variables are allowed to vary). Partial derivatives are used in vector calculus and differential geometry.
Integration by substitution is the chain rule in reverse.
NOTE: the final location is section specific. Section 1 (morning) is in SILV 703, Section 11 (afternoon) is in CANT 200
The concept of limit formalizes the notion of closeness of the function values to a certain value "near" a certain point. Limits behave well with respect to arithmetic--usually. Division by zero is always a problem, and we can't make conclusions about nonexistent limits!
Application of definite integrals,we will explore some of the many application of definite integral by using it to calculate areas between two curves, volumes, length of curves, and several other application.
In mathematics, a partial derivative of a function of several variables is its derivative with respect to one of those variables, with the others held constant (as opposed to the total derivative, in which all variables are allowed to vary). Partial derivatives are used in vector calculus and differential geometry.
Integration by substitution is the chain rule in reverse.
NOTE: the final location is section specific. Section 1 (morning) is in SILV 703, Section 11 (afternoon) is in CANT 200
The concept of limit formalizes the notion of closeness of the function values to a certain value "near" a certain point. Limits behave well with respect to arithmetic--usually. Division by zero is always a problem, and we can't make conclusions about nonexistent limits!
this is my presentation on "Operators and Expressions" .this is my beginner days trial, so i cant make it perfect ,,,but surely say that it is most helpful for you
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it covers the following topics:
Java Evolution
Overview
Constants, variables & data types
Operators and expressions
Decision making and branching
Decision making and looping
Classes, objects & methods
Arrays, Strings and Vectors
Interface
Packages
Multi-threading
Managing errors and exceptions
Applet programming
Instructions for Submissions thorugh G- Classroom.pptxJheel Barad
This presentation provides a briefing on how to upload submissions and documents in Google Classroom. It was prepared as part of an orientation for new Sainik School in-service teacher trainees. As a training officer, my goal is to ensure that you are comfortable and proficient with this essential tool for managing assignments and fostering student engagement.
How to Split Bills in the Odoo 17 POS ModuleCeline George
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The French Revolution, which began in 1789, was a period of radical social and political upheaval in France. It marked the decline of absolute monarchies, the rise of secular and democratic republics, and the eventual rise of Napoleon Bonaparte. This revolutionary period is crucial in understanding the transition from feudalism to modernity in Europe.
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Model Attribute Check Company Auto PropertyCeline George
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How to Make a Field invisible in Odoo 17Celine George
It is possible to hide or invisible some fields in odoo. Commonly using “invisible” attribute in the field definition to invisible the fields. This slide will show how to make a field invisible in odoo 17.
How to Create Map Views in the Odoo 17 ERPCeline George
The map views are useful for providing a geographical representation of data. They allow users to visualize and analyze the data in a more intuitive manner.
Read| The latest issue of The Challenger is here! We are thrilled to announce that our school paper has qualified for the NATIONAL SCHOOLS PRESS CONFERENCE (NSPC) 2024. Thank you for your unwavering support and trust. Dive into the stories that made us stand out!
The Art Pastor's Guide to Sabbath | Steve ThomasonSteve Thomason
What is the purpose of the Sabbath Law in the Torah. It is interesting to compare how the context of the law shifts from Exodus to Deuteronomy. Who gets to rest, and why?
2. WHAT IS EXPLICIT/IMPLICIT FUNCTION?
The explicit function is a function in which the
dependent variable has been given “explicitly” in terms of
the independent variable. Or it is a function in which the
dependent variable is expressed in terms of some
independent variables.
The Implicit function is a function in which the
dependent variable has not been given “explicitly” in
terms of the independent variable. Or it is a function in
which the dependent variable is not expressed in terms
of some independent variables.
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3. EXPLICIT/IMPLICIT FUNCTION
Examples of explicit function
Explicit functions:
y = 3x – 2
y = x2 + 5
Examples of implicit function
Implicit functions:
y2 + 2yx 4x2 = 0
y5 - 3y2x2 + 2 = 0
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4. WHY IMPLICIT DIFFERENTIATION?
When an applied problem involves an equation not
in explicit form, implicit differentiation is used to
locate extrema or to find rates of change.
Implicit Differentiation. In many examples,
especially the ones derived from differential
equations, the variables involved are not linked to
each other in an explicit way. Most of the time, they
are linked through an implicit formula, like F(x,y)
=0. Once x is fixed, we may find y through
numerical computations.
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5. PROCESS FOR IMPLICIT DIFFERENTIATION
To find dy/dx
Differentiate both sides with respect to x (y is
assumed to be a function of x, so d/dx)
Collect like terms (all dy/dx on the same side,
everything else on the other side)
Factor out the dy/dx and solve for dy/dx
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6. EXAMPLE
Find dy/dx if 3xy + 4y2 = 10
Differentiate both sides with respect to x:
Use the product rule for (3x)(y)
(The derivative of y is dy/dx)
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7. Since y is assumed to be some function of x, use the
chain rule for 4y2
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10. WHAT IS TOTAL DERIVATIVE?
he total derivative is the derivative with respect to
of the function that depends on the variable not only
directly but also via the intermediate variables . It
can be calculated using the formula.
This rule is called the chain rule for the partial
derivatives of functions of functions.
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11. TOTAL DERIVATIVE
If w = f(x, y, z, ...) is a continuous function of n
variables x, y, z, ..., with continuous partial
derivatives ∂w/∂x, ∂w/∂y, ∂w/∂z, ... and if x, y, z, ...
are differentiable functions x = x(t), y = y(t) , z = z(t),
etc. of a variable t, then the total derivative of w
with respect to t is given by
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12. Similarly, if w = f(x, y, z, ...) is a continuous function of n
variables x, y, z, ..., with continuous partial derivatives
∂w/∂x, ∂w/∂y, ∂w/∂z, ... and if x, y, z, ... are differentiable
functions of m independent variables r, s, t ... , then
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13. Note the similarity between total differentials and total
derivatives. The total derivative above can be obtained
by dividing the total differential by dt,dr,ds
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14. As a special application of the chain rule let us consider
the relation defined by the two equations
z = f(x, y); y = g(x)
Here, z is a function of x and y while y in turn is a function
of x. Thus z is really a function of the single variable x. If
we apply the chain rule we get
which is the total derivative of z with respect to x.
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