Let’s first look at the graph in
[link] to get a better idea of the area of interest.
The intervals are
and
Note that
is increasing on the interval
so a left-endpoint approximation gives us the lower sum. A left-endpoint approximation is the Riemann sum
We have
The use of sigma (summation) notation of the form
is useful for expressing long sums of values in compact form.
For a continuous function defined over an interval
the process of dividing the interval into
n equal parts, extending a rectangle to the graph of the function, calculating the areas of the series of rectangles, and then summing the areas yields an approximation of the area of that region.
The width of each rectangle is
Riemann sums are expressions of the form
and can be used to estimate the area under the curve
Left- and right-endpoint approximations are special kinds of Riemann sums where the values of
are chosen to be the left or right endpoints of the subintervals, respectively.
Riemann sums allow for much flexibility in choosing the set of points
at which the function is evaluated, often with an eye to obtaining a lower sum or an upper sum.
Key equations
Properties of Sigma Notation
Sums and Powers of Integers
Left-Endpoint Approximation
Right-Endpoint Approximation
State whether the given sums are equal or unequal.
and
and
and
and
a. They are equal; both represent the sum of the first 10 whole numbers. b. They are equal; both represent the sum of the first 10 whole numbers. c. They are equal by substituting
d. They are equal; the first sum factors the terms of the second.
Communication is effective because it allows individuals to share ideas, thoughts, and information with others.
effective communication can lead to improved outcomes in various settings, including personal relationships, business environments, and educational settings. By communicating effectively, individuals can negotiate effectively, solve problems collaboratively, and work towards common goals.
it starts up serve and return practice/assessments.it helps find voice talking therapy also assessments through relaxed conversation.
miss
Every time someone flushes a toilet in the apartment building, the person begins to jumb back automatically after hearing the flush, before the water temperature changes. Identify the types of learning, if it is classical conditioning identify the NS, UCS, CS and CR. If it is operant conditioning, identify the type of consequence positive reinforcement, negative reinforcement or punishment
nature is an hereditary factor while nurture is an environmental factor which constitute an individual personality. so if an individual's parent has a deviant behavior and was also brought up in an deviant environment, observation of the behavior and the inborn trait we make the individual deviant.
Samuel
I am taking this course because I am hoping that I could somehow learn more about my chosen field of interest and due to the fact that being a PsyD really ignites my passion as an individual the more I hope to learn about developing and literally explore the complexity of my critical thinking skills
hello. autism is a umbrella term. autistic kids have different disorder overlapping. for example. a kid may show symptoms of ADHD and also learning disabilities.
before treatment please make sure the kid doesn't have physical disabilities like hearing..vision..speech problem. sometimes these
Jharna
continue..
sometimes due to these physical problems..the diagnosis may be misdiagnosed.
treatment for autism.
well it depends on the severity.
since autistic kids have problems in communicating and adopting to the environment.. it's best to expose the child in situations where the child
Jharna
child interact with other kids under doc supervision.
play therapy.
speech therapy.
Engaging in different activities that activate most parts of the brain.. like drawing..painting. matching color board game.
string and beads game.
the more you interact with the child the more effective
Jharna
results you'll get..
please consult a therapist to know what suits best on your child.
and last as a parent. I know sometimes it's overwhelming to guide a special kid.
but trust the process and be strong and patient as a parent.
Jharna
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