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SECONDARY
CALCULUS AND ANALYSIS
CALCULUS 1
POLYNOMIAL GRAPHS
Secondary
Calculus and Analysis
Precalculus
Calculus 1
Limits and continuity
Derivatives
Integrals
Polynomial graphs
Exponential models
Transformations of functions
Analyzing functions
Calculus 2
Algebra
Geometry
Statistics and Probability
Math Word Problem
Other
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Recent Polynomial Graphs Answers
Polynomial graphs
asked 2021-02-20
Describe any similarities and differences. Refer to the end behaviour, local maximum and local minimum points, and maximum and minimum points.
a) Sketch graphs of
\(\displaystyle{y}={\sin{\ }}{x}\)
and
\(\displaystyle{y}={\cos{\ }}{x}.\)
b) Compare the graph of a periodic function to the graph of a polynomial function.
Polynomial graphs
asked 2021-02-15
Using calculus, it can be shown that the tangent function can be approximated by the polynomial
\(\displaystyle{\tan{\ }}{x}\ \approx\ {x}\ +\ {\frac{{{2}{x}^{{{3}}}}}{{{3}!}}}\ +\ {\frac{{{16}{x}^{{{5}}}}}{{{5}!}}}\)
where x is in radians. Use a graphing utility to graph the tangent function and its polynomial approximation in the same viewing window. How do the graphs.
Polynomial graphs
asked 2021-02-02
(a) find the Maclaurin polynomial
\(\displaystyle{P}_{{{3}}}{\left({x}\right)}\)
for PSKf(x), (b) complete the following PSKx: -0.75, -0.50, -0.25, 0, 0.25, 0.50, 0.75 for f(x) and P_{3}(x) and (c) sketch the graphs of f(x) and
\(\displaystyle{P}_{{{3}}}{\left({x}\right)}\)
on the same set of coordinate axes.
\(\displaystyle{f{{\left({x}\right)}}}={\arctan{{x}}}\)
Polynomial graphs
asked 2021-01-30
Find the quadratic polynomial
\(\displaystyle{g{{\left({x}\right)}}}-{a}{x}^{{{2}}}\ +\ {b}{x}\ +\ {c}\ \text{which best fits the function}\ {f{{\left({x}\right)}}}={e}^{{{x}}}\ \text{at}\ {x}={0},\ \text{in the sense that}\ {g{{\left({0}\right)}}}={f{{\left({0}\right)}}},\ \text{and}\ {g}'{\left({0}\right)}={f}'{\left({0}\right)},\ \text{and}\ {g}{''}{\left({0}\right)}={f}{''}{\left({0}\right)}.\)
Using a computer or calculator, sketch graphs of f and g on the same axes. What do you notice?
Polynomial graphs
asked 2020-11-01
For the following exercise, for each polynomial
\(\displaystyle{f{{\left({x}\right)}}}=\ {\frac{{{1}}}{{{2}}}}{x}^{{{2}}}\ -\ {1}\)
: a) find the degree, b) find the zeros, if any, c) find the y-intercept(s), if any, d) use the leading coefficient to determine the graph’s end behavior, e) determine algebraically whether the polynomial is even, odd, or neither.
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