Question

Prove by induction that $(k + 2)^{k + 1} \leq (k+1)^{k +2}$

score 163 · Answer 1 · 2026-04-13 14:43:48

163

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Prove by induction that $(k + 2)^{k + 1} \leq (k+1)^{k +2}$

Published on 13 Apr 2026 - 14:43

score 83 · Answer 2 · 2026-04-10 22:06:13

83

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Free Response Question About Product Sales Function (Integration)

Published on 10 Apr 2026 - 22:06

score 39 · Answer 3 · 2026-04-16 02:35:10

39

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Tangent map is continuous when derivative is not, given infinite-dimensional Banach space

Published on 16 Apr 2026 - 2:35

score 459 · Answer 4 · 2026-04-15 23:33:32

459

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Find the sum of the series $\sum_{n=1}^{\infty}\frac{1}{2^n-1}.$

Published on 15 Apr 2026 - 23:33

score 87 · Answer 5 · 2026-03-25 22:06:30

87

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If $u_x=0$ and $u_y = 0$ on a open, connected set. Then $u$ is a constant on the set.

Published on 25 Mar 2026 - 22:06

score 59 · Answer 6 · 2026-04-12 12:44:39

59

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Finding $\alpha$ and $\beta$ so that function becomes continuous

Published on 12 Apr 2026 - 12:44

score 399 · Answer 7 · 2026-04-12 05:10:38

399

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Two equivalent definitions of the derivative?

Published on 12 Apr 2026 - 5:10

score 48 · Answer 8 · 2026-04-11 08:05:27

48

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Connection between the proofs of two lemmas in calculus

Published on 11 Apr 2026 - 8:05

score 67 · Answer 9 · 2026-04-16 21:51:28

67

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Minimum, maximum and $||f_n||_\infty$ of $f_n(x) = x^{\frac{n}{2}}e^{-nx}$

Published on 16 Apr 2026 - 21:51

score 68 · Answer 10 · 2026-04-15 19:39:26

68

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I have some unclear things in mind related to the Riemann integrals theorem for the uniform convergent series and uniform convergent string.

Published on 15 Apr 2026 - 19:39

score 678 · Answer 11 · 2026-04-10 18:59:55

678

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How to prove this definite integral does not depend on the parameter?

Published on 10 Apr 2026 - 18:59

score 87 · Answer 12 · 2026-04-15 11:21:04

87

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Pointwise and uniform convergence of $\sum_{n=0}^\infty x^n(1-x)$

Published on 15 Apr 2026 - 11:21

score 144 · Answer 13 · 2026-04-17 09:34:46

144

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Chain rule problem: given $f(x)=\sqrt{4x+7}$ and $g(x)=e^{x+4}$, compute $f(g(x))'$.

Published on 17 Apr 2026 - 9:34

score 4.3k · Answer 14 · 2026-04-16 13:14:42

4.3k

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Integral of $\int{\frac{\cos^4x + \sin^4x}{\sqrt{1 + \cos 4x}}dx}$

Published on 16 Apr 2026 - 13:14

score 74 · Answer 15 · 2026-04-17 12:59:19

74

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Justify the given limit: $\lim_{n\to\infty}$ ${\sqrt[8]{n^2+1}-\sqrt[4]{n+1}}=0$

Published on 17 Apr 2026 - 12:59

List Question

Prove by induction that $(k + 2)^{k + 1} \leq (k+1)^{k +2}$

Free Response Question About Product Sales Function (Integration)

Tangent map is continuous when derivative is not, given infinite-dimensional Banach space

Find the sum of the series $\sum_{n=1}^{\infty}\frac{1}{2^n-1}.$

If $u_x=0$ and $u_y = 0$ on a open, connected set. Then $u$ is a constant on the set.

Finding $\alpha$ and $\beta$ so that function becomes continuous

Two equivalent definitions of the derivative?

Connection between the proofs of two lemmas in calculus

Minimum, maximum and $||f_n||_\infty$ of $f_n(x) = x^{\frac{n}{2}}e^{-nx}$

I have some unclear things in mind related to the Riemann integrals theorem for the uniform convergent series and uniform convergent string.

How to prove this definite integral does not depend on the parameter?

Pointwise and uniform convergence of $\sum_{n=0}^\infty x^n(1-x)$

Chain rule problem: given $f(x)=\sqrt{4x+7}$ and $g(x)=e^{x+4}$, compute $f(g(x))'$.

Integral of $\int{\frac{\cos^4x + \sin^4x}{\sqrt{1 + \cos 4x}}dx}$

Justify the given limit: $\lim_{n\to\infty}$ ${\sqrt[8]{n^2+1}-\sqrt[4]{n+1}}=0$

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