Question

Finding $\lim_{n\to \infty} n^{b-a}\frac{1^a+2^a+\cdots +n^a}{1^b+2^b+\cdots +n^b}$

score 109 · Answer 1 · 2019-07-13 11:22:37

109

Views

Finding $\lim_{n\to \infty} n^{b-a}\frac{1^a+2^a+\cdots +n^a}{1^b+2^b+\cdots +n^b}$

Published on 13 Jul 2019 - 11:22

score 232 · Answer 2 · 2026-03-27 03:41:14

232

Views

Can we cancel out $1$ after replacing $e^x$ in $e^x-1$ by its Taylor expansion when calculating a limit?

Published on 27 Mar 2026 - 3:41

score 411 · Answer 3 · 2019-07-15 19:46:26

411

Views

Solving the following limit without L'Hospital's rule: $\lim_{x\to 0} \frac{\sin(x^2+2)-\sin(x+2)}{x} $

Published on 15 Jul 2019 - 19:46

score 121 · Answer 4 · 2019-07-20 14:27:11

121

Views

Evaluate the limit the following series

Published on 20 Jul 2019 - 14:27

score 44 · Answer 5 · 2019-07-20 21:19:12

44

Views

Does $\frac{a_n}{x_n} \approx L$ for sufficiently large $n$ $\implies a_n \approx Lx_n$ for sufficiently large $n$?

Published on 20 Jul 2019 - 21:19

score 82 · Answer 6 · 2026-03-27 04:03:28

How do we obtain the following: $\lim_{n \to \infty}\frac{\ln{n^n}}{\ln{n!!}}=\lim_{n \to \infty}\frac{\ln{n^n}-\ln(n-2)^{n-2}}{\ln{n!!}-\ln(n-2)!!}$

score 81 · Answer 7 · 2019-07-26 00:55:45

81

Views

Getting the limit for a ratio of logarithms functions with different base

Published on 26 Jul 2019 - 0:55

score 5.9k · Answer 8 · 2019-07-28 16:18:40

5.9k

Views

When Is the Squeeze(Sandwich) Theorem Used?

Published on 28 Jul 2019 - 16:18

score 148 · Answer 9 · 2019-07-31 02:23:27

148

Views

Show that $\lim_{x\to \frac{\pi}{2}} \frac{1}{\big(x-\frac{\pi}{2}\big)}+{\tan(x)}=0$.

Published on 31 Jul 2019 - 2:23

score 94 · Answer 10 · 2019-08-01 06:19:27

94

Views

prove the following series doesn't converge : $a_n = 2^n \cdot \sin(\frac 1n) $

Published on 01 Aug 2019 - 6:19

score 77 · Answer 11 · 2019-08-02 17:37:02

77

Views

Evaluate $\lim \limits_{x \to 2} \frac{\sqrt{x+7} - \sqrt[\leftroot{5}\uproot{0}3]{4x+19}}{x-2}$

Published on 02 Aug 2019 - 17:37

score 647 · Answer 12 · 2019-08-02 22:53:05

647

Views

True or false limit questions with explanation

Published on 02 Aug 2019 - 22:53

score 25 · Answer 13 · 2019-08-03 04:47:18

25

Views

Limit of $(x+k)(F(x)-F(x-a)$ as $x \rightarrow \infty$

Published on 03 Aug 2019 - 4:47

score 124 · Answer 14 · 2019-08-04 05:37:26

124

Views

If $\lim \limits_{x \to 1} \frac{f(x)+2}{x-1} = 3$, compute: $\lim \limits_{x \to -1} \frac{(f(-x))^2-4}{x^2-1}$

Published on 04 Aug 2019 - 5:37

score 74 · Answer 15 · 2019-08-04 17:22:45

74

Views

Find the $\lim_{x \to \infty} \Big(\frac{x}{e} - x\Big(\frac{x}{x+1}\Big)^x\Big)$

Published on 04 Aug 2019 - 17:22

List Question

Finding $\lim_{n\to \infty} n^{b-a}\frac{1^a+2^a+\cdots +n^a}{1^b+2^b+\cdots +n^b}$

Can we cancel out $1$ after replacing $e^x$ in $e^x-1$ by its Taylor expansion when calculating a limit?

Solving the following limit without L'Hospital's rule: $\lim_{x\to 0} \frac{\sin(x^2+2)-\sin(x+2)}{x} $

Evaluate the limit the following series

Does $\frac{a_n}{x_n} \approx L$ for sufficiently large $n$ $\implies a_n \approx Lx_n$ for sufficiently large $n$?

How do we obtain the following: $\lim_{n \to \infty}\frac{\ln{n^n}}{\ln{n!!}}=\lim_{n \to \infty}\frac{\ln{n^n}-\ln(n-2)^{n-2}}{\ln{n!!}-\ln(n-2)!!}$

Getting the limit for a ratio of logarithms functions with different base

When Is the Squeeze(Sandwich) Theorem Used?

Show that $\lim_{x\to \frac{\pi}{2}} \frac{1}{\big(x-\frac{\pi}{2}\big)}+{\tan(x)}=0$.

prove the following series doesn't converge : $a_n = 2^n \cdot \sin(\frac 1n) $

Evaluate $\lim \limits_{x \to 2} \frac{\sqrt{x+7} - \sqrt[\leftroot{5}\uproot{0}3]{4x+19}}{x-2}$

True or false limit questions with explanation

Limit of $(x+k)(F(x)-F(x-a)$ as $x \rightarrow \infty$

If $\lim \limits_{x \to 1} \frac{f(x)+2}{x-1} = 3$, compute: $\lim \limits_{x \to -1} \frac{(f(-x))^2-4}{x^2-1}$

Find the $\lim_{x \to \infty} \Big(\frac{x}{e} - x\Big(\frac{x}{x+1}\Big)^x\Big)$

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