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Limit $\lim_{x\to\infty}(x^3+x^2)^{1/3}-(x^4-x^3)^{1/4}$

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#calculus #limits
1.4k
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Evaluate: $\lim_{x \to \pi/4}\frac{8-\sqrt{2}(\sin x+\cos x)^5}{1-\sin 2x}$ without L'Hopitals

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#real-analysis #limits #limits-without-lhopital #indeterminate-forms
261
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Prove that a function is affine

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#calculus #real-analysis #limits #derivatives
613
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Exactly when does a limit of a rational function exist?

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#calculus #limits #rational-functions
534
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The derivative of $\arcsin(x)$ at $x=1$

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#calculus #limits #trigonometry #inverse-function
1.5k
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Why is the Indefinite Integral of a Step Function and continuous?

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#calculus #real-analysis #integration #limits #continuity
100
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Does $\lim_{x\to\infty} f'(x) = 0$ implies $\lim_{x\to\infty} f(x)$ exists finite?

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#calculus #limits #derivatives
66
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$ \lim_{c \to a} \int_0^c f(x,c) \space dx $

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#calculus #limits #improper-integrals
199
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How Gelfond find his limit for $\exp(\pi) $?

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#limits #roots #fixed-point-theorems #pi
126
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Absolute value of regulated function

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#calculus #limits
46
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Limit of the following integration

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#limits
430
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Find $\lim_{x\rightarrow0}\frac{x}{[x]}$

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#calculus #limits
232
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Can someone help me do this limit? $ \lim_{n\to\infty} \frac{n!\times(2n)!}{(3n)!}$

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#calculus #limits #factorial
77
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Why am I getting the sign of this limit wrong?

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#limits
62
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Convergence of $\sum_{i\ge 1} (e^{(-1)^i\sin (\frac{1}{i})}-1)$

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#calculus #real-analysis #sequences-and-series #limits #convergence-divergence

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