Question

Directional derivative of $f(x,y ) = \frac{xy^2}{x^2+y^4}, (x,y)\neq (0,0)$ & otherwise $0$

score 609 · Answer 1 · 2019-02-04 14:55:53

609

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Directional derivative of $f(x,y ) = \frac{xy^2}{x^2+y^4}, (x,y)\neq (0,0)$ & otherwise $0$

Published on 04 Feb 2019 - 14:55

score 657 · Answer 2 · 2019-02-05 15:29:01

657

Views

Two different answers with different methods in solving limits.

Published on 05 Feb 2019 - 15:29

score 145 · Answer 3 · 2026-03-22 14:13:40

145

Views

$a_n=(-1)^{n-1}, \; s_n=\sum_{i=1}^{n}a_i$ then find $ \lim_{n\to \infty}\frac{s_1+s_2+\dots s_n}{n}$

Published on 22 Mar 2026 - 14:13

score 118 · Answer 4 · 2019-02-05 21:05:17

118

Views

help with solving a limit with logarithms

Published on 05 Feb 2019 - 21:05

score 1.3k · Answer 5 · 2026-03-26 09:58:02

1.3k

Views

Radius of convergence of power series $\sum_{n=0}^{\infty} n!x^{n^2}$

Published on 26 Mar 2026 - 9:58

score 83 · Answer 6 · 2019-02-06 15:05:34

83

Views

How to compute $\lim_{x\to \infty} \frac{\ln(1+x)}{\ln x} $?

Published on 06 Feb 2019 - 15:05

score 109 · Answer 7 · 2019-02-08 22:56:00

109

Views

Solving limit without applying L'Hospital's rule

Published on 08 Feb 2019 - 22:56

score 77 · Answer 8 · 2019-02-09 11:06:57

77

Views

Calculate limit with squares $\lim_{n \to \infty}\left(\sqrt[3]{n^3+2n-1}-\sqrt[3]{n^3+2n-3}\right)^6 \cdot (1+3n+2n^3)^4$

Published on 09 Feb 2019 - 11:06

score 42 · Answer 9 · 2019-02-11 04:51:07

42

Views

how to define the functions $f(x)$ and $g(x)$ by a given equation

Published on 11 Feb 2019 - 4:51

score 50 · Answer 10 · 2019-02-11 14:31:38

50

Views

help with finding that $f(x) =g(x)$

Published on 11 Feb 2019 - 14:31

score 452 · Answer 11 · 2019-02-11 17:40:53

452

Views

$\lim_{x\to0}\frac{\arcsin x-\sin x}{x^3}$ without series or L'Hospital

Published on 11 Feb 2019 - 17:40

score 310 · Answer 12 · 2019-02-11 20:57:05

310

Views

Evaluate: $\lim_{x\to0}\left (\frac{4^{\tan(x)}+ \cos(x)}{2}\right)^{\cot(x)}$

Published on 11 Feb 2019 - 20:57

score 75 · Answer 13 · 2019-02-13 19:23:28

75

Views

$\lim _{x\to 0}\left(\sin\left(x\right)\cos\left(\frac{5}{x}\right)\right)$ Can I apply Sandwich Theorem to this limit?

Published on 13 Feb 2019 - 19:23

score 327 · Answer 14 · 2019-02-13 21:27:11

327

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Proof that $\lim_{x \to 0} \frac{\sin(x) - x}{x^2} = 0$ (Without L'Hospital)

Published on 13 Feb 2019 - 21:27

score 1.2k · Answer 15 · 2019-02-14 00:16:27

1.2k

Views

Showing that $\lim_{x\to 0} x\log{x}= 0$ without using L'Hopital's rule

Published on 14 Feb 2019 - 0:16

List Question

Directional derivative of $f(x,y ) = \frac{xy^2}{x^2+y^4}, (x,y)\neq (0,0)$ & otherwise $0$

Two different answers with different methods in solving limits.

$a_n=(-1)^{n-1}, \; s_n=\sum_{i=1}^{n}a_i$ then find $ \lim_{n\to \infty}\frac{s_1+s_2+\dots s_n}{n}$

help with solving a limit with logarithms

Radius of convergence of power series $\sum_{n=0}^{\infty} n!x^{n^2}$

How to compute $\lim_{x\to \infty} \frac{\ln(1+x)}{\ln x} $?

Solving limit without applying L'Hospital's rule

Calculate limit with squares $\lim_{n \to \infty}\left(\sqrt[3]{n^3+2n-1}-\sqrt[3]{n^3+2n-3}\right)^6 \cdot (1+3n+2n^3)^4$

how to define the functions $f(x)$ and $g(x)$ by a given equation

help with finding that $f(x) =g(x)$

$\lim_{x\to0}\frac{\arcsin x-\sin x}{x^3}$ without series or L'Hospital

Evaluate: $\lim_{x\to0}\left (\frac{4^{\tan(x)}+ \cos(x)}{2}\right)^{\cot(x)}$

$\lim _{x\to 0}\left(\sin\left(x\right)\cos\left(\frac{5}{x}\right)\right)$ Can I apply Sandwich Theorem to this limit?

Proof that $\lim_{x \to 0} \frac{\sin(x) - x}{x^2} = 0$ (Without L'Hospital)

Showing that $\lim_{x\to 0} x\log{x}= 0$ without using L'Hopital's rule

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