Question

Proof of Fundamental Theorem of Calculus using delta-epsilon definition

score 357 · Answer 1 · 2026-04-07 17:37:46

357

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Proof of Fundamental Theorem of Calculus using delta-epsilon definition

Published on 07 Apr 2026 - 17:37

score 1k · Answer 2 · 2021-07-29 05:45:28

1k

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Choice of $\delta$ for "brute force" proof of continuity of exponential function $e^x$

Published on 29 Jul 2021 - 5:45

score 35 · Answer 3 · 2026-03-29 07:33:44

35

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Need help proving theorem for limits of multivariable functions (parabola approach)

Published on 29 Mar 2026 - 7:33

score 117 · Answer 4 · 2021-08-03 06:17:45

117

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Can it be concluded that $z_ n \to z$ as $n \to \infty\ $?

Published on 03 Aug 2021 - 6:17

score 38 · Answer 5 · 2021-08-06 17:57:15

38

Views

The equivalence of two situations about convergence of the sequence.

Published on 06 Aug 2021 - 17:57

score 83 · Answer 6 · 2021-08-12 17:23:11

83

Views

Scaled $\epsilon$ in $\epsilon$-$\delta$ proofs

Published on 12 Aug 2021 - 17:23

score 382 · Answer 7 · 2021-08-16 23:50:47

382

Views

Proof verification: sequential definition of limits of functions implies $\epsilon - \delta$ definition

Published on 16 Aug 2021 - 23:50

score 90 · Answer 8 · 2021-08-17 04:59:33

90

Views

How to show alternate definition of holomorphic holds: there exists $a$ such that $f(z_{0}+h)-f(z_{0})-a h=h \psi(h)$?

Published on 17 Aug 2021 - 4:59

score 114 · Answer 9 · 2021-08-18 11:33:09

114

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Given the function $f(x,y)=\frac{5xy^2}{x^2+y^2}$, argue analytically, if the discontinuity of $f$ at $(0,0)$ is avoidable or unavoidable.

Published on 18 Aug 2021 - 11:33

score 126 · Answer 10 · 2021-08-19 17:10:42

126

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Do we have $|\frac{f(x)-f(a)}{x-a} - f'(a)| \geq |f(x)- f(a)|$?

Published on 19 Aug 2021 - 17:10

score 84 · Answer 11 · 2021-08-22 03:26:34

84

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Prove that the limit $\lim_{(x,y)\to(0,0)} \frac{y^4}{\sqrt{3x^2+y^2}}\cos(\frac{1}{x})$ exists using $\epsilon \text{ and } \delta$ definition

Published on 22 Aug 2021 - 3:26

score 114 · Answer 12 · 2021-08-23 20:20:17

114

Views

Prove using epislon and delta that the limit of $f(x,y)$ as $(x,y)$ goes to $(0,0)$ does not exist

Published on 23 Aug 2021 - 20:20

score 163 · Answer 13 · 2021-08-24 07:55:57

163

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Constructive proof of: If $\lim_{x \to a}(f \cdot g) (x) = L$ and $\lim_{x \to a}f (x) = \frac{L}{K}$ for $K \neq 0$, then $\lim_{x \to a}g (x)=K$.

Published on 24 Aug 2021 - 7:55

score 100 · Answer 14 · 2021-08-25 06:52:52

100

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If $\lim_{x \to a} f(x) = \infty$ and $\lim_{x \to a} g(x) = c$, prove that $\lim_{x \to a} f(x)g(x) = \infty$

Published on 25 Aug 2021 - 6:52

score 190 · Answer 15 · 2021-08-28 16:51:03

190

Views

Proof of the product rule of limits

Published on 28 Aug 2021 - 16:51

List Question

Proof of Fundamental Theorem of Calculus using delta-epsilon definition

Choice of $\delta$ for "brute force" proof of continuity of exponential function $e^x$

Need help proving theorem for limits of multivariable functions (parabola approach)

Can it be concluded that $z_ n \to z$ as $n \to \infty\ $?

The equivalence of two situations about convergence of the sequence.

Scaled $\epsilon$ in $\epsilon$-$\delta$ proofs

Proof verification: sequential definition of limits of functions implies $\epsilon - \delta$ definition

How to show alternate definition of holomorphic holds: there exists $a$ such that $f(z_{0}+h)-f(z_{0})-a h=h \psi(h)$?

Given the function $f(x,y)=\frac{5xy^2}{x^2+y^2}$, argue analytically, if the discontinuity of $f$ at $(0,0)$ is avoidable or unavoidable.

Do we have $|\frac{f(x)-f(a)}{x-a} - f'(a)| \geq |f(x)- f(a)|$?

Prove that the limit $\lim_{(x,y)\to(0,0)} \frac{y^4}{\sqrt{3x^2+y^2}}\cos(\frac{1}{x})$ exists using $\epsilon \text{ and } \delta$ definition

Prove using epislon and delta that the limit of $f(x,y)$ as $(x,y)$ goes to $(0,0)$ does not exist

Constructive proof of: If $\lim_{x \to a}(f \cdot g) (x) = L$ and $\lim_{x \to a}f (x) = \frac{L}{K}$ for $K \neq 0$, then $\lim_{x \to a}g (x)=K$.

If $\lim_{x \to a} f(x) = \infty$ and $\lim_{x \to a} g(x) = c$, prove that $\lim_{x \to a} f(x)g(x) = \infty$

Proof of the product rule of limits

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