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Find the Maclaurin polynomial of degree $5$ for $f(x) = x\cos(x^2)$.

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#calculus #sequences-and-series #taylor-expansion
105
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Does comparing a function against $x^N$ ensure $N$ times differentiable?

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#calculus #derivatives #taylor-expansion
462
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If a series converges to zero, does this imply that the leading terms are zero? Or under what conditions would this be necessary?

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#real-analysis #sequences-and-series #convergence-divergence #power-series #taylor-expansion
26
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How to solve for x in an inequality that contains factorials?

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#inequality #taylor-expansion #factorial
55
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Special integral, Help me solve it please!

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#integration #taylor-expansion #gamma-function #complex-integration
85
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Series Expansion and Big-Oh Notation: Expanding $\sqrt{x^2+\mathcal{O}(x^3)}$ to get $x+\mathcal{O}(x^{3/2})$

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#asymptotics #power-series #taylor-expansion #binomial-theorem
87
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Is there a way to represent functions using circles, similar to how Taylor series work?

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#power-series #taylor-expansion #circles #approximation
136
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Geometric Series to approximate power series expansion

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#sequences-and-series #probability-theory #taylor-expansion #geometric-series #geometric-progressions
88
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how to solve the differential equation $\frac{kx^t}{v^2} + 1=\frac{dv}{dx}$

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#real-analysis #calculus #ordinary-differential-equations #taylor-expansion
65
Views

I need help clearing this equation

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#sequences-and-series #taylor-expansion
173
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Taylor Series for $x^2 \ln(1 + \frac{1}{x})$ at $x = 0$.

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#limits #taylor-expansion
75
Views

Why is $f^n(\xi(x))$ continuous over $x$?

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#analysis #numerical-methods #taylor-expansion
46
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How to prove the following statements using the Taylor polynomial.

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#limits #taylor-expansion
12
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Use of Taylor Polynomial remainder to show size of error.

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#real-analysis #integration #taylor-expansion
30
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Prove that $|R_{n,0}| \leq \frac{|x|^{n+1}}{(n+1)(x+1)}$

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#real-analysis #taylor-expansion

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