Question

Prove $\lim \limits_{h \to 0} \frac{a^h-1}{h} = \ln (a)$ without using L'hospital's.

score 131 · Answer 1 · 2026-04-15 01:33:45

131

Views

Prove $\lim \limits_{h \to 0} \frac{a^h-1}{h} = \ln (a)$ without using L'hospital's.

Published on 15 Apr 2026 - 1:33

score 40 · Answer 2 · 2026-04-15 10:29:30

40

Views

Trouble with integration of following: $ \int^\infty_0 \exp(a(x)+b(x))a'(x)dx$

Published on 15 Apr 2026 - 10:29

score 131 · Answer 3 · 2026-04-12 08:53:10

131

Views

Is there a proof $e^ae^b=e^{a+b}$ using its power series expansion?

Published on 12 Apr 2026 - 8:53

score 87 · Answer 4 · 2026-04-12 09:23:28

87

Views

Simplifying an arbitrary constant.

Published on 12 Apr 2026 - 9:23

score 145 · Answer 5 · 2026-04-17 03:11:26

145

Views

Hints on solving $x^{2x}-(x^2+x)x^x+x^3=0$

Published on 17 Apr 2026 - 3:11

score 130 · Answer 6 · 2026-04-14 18:40:05

130

Views

How to solve $2^{\sin^2(x)}=\cos(x)$

Published on 14 Apr 2026 - 18:40

score 156 · Answer 7 · 2026-04-16 21:18:52

156

Views

Solving $|x-1|^{\log_2(4-x)} \le|x-1|^{\log_2 (1+x)}$

Published on 16 Apr 2026 - 21:18

score 111 · Answer 8 · 2026-04-12 03:19:29

111

Views

Exponential function using binomial approach and approximation by power series, both using python. Why different results?

Published on 12 Apr 2026 - 3:19

score 56 · Answer 9 · 2026-04-12 08:34:02

56

Views

A Series Representation for the Natural Logarithm Not Comprised of Exponential Terms

Published on 12 Apr 2026 - 8:34

score 35 · Answer 10 · 2026-04-12 02:03:12

35

Views

Finding the value of this exponential limit

Published on 12 Apr 2026 - 2:03

score 87 · Answer 11 · 2026-04-14 13:35:09

87

Views

Extension of a well known formula for the Euler number into the complex domain

Published on 14 Apr 2026 - 13:35

score 137 · Answer 12 · 2026-04-14 22:18:29

137

Views

Minimizing a function $f$ of the form $f(x)=\prod_if(x_i)$, is it possible to ensure $x_1,\ldots,x_j$ minimizes $\prod_i^jf(x_i)$?

Published on 14 Apr 2026 - 22:18

score 95 · Answer 13 · 2026-04-14 19:28:59

95

Views

Solving for i in mortgage payment formula in M = P [ i(1 + i)^n ] / [ (1 + i)^n – 1].

Published on 14 Apr 2026 - 19:28

score 48 · Answer 14 · 2026-04-13 21:24:39

48

Views

Inequality involving exponentials and integrals

Published on 13 Apr 2026 - 21:24

score 115 · Answer 15 · 2026-04-12 01:38:01

115

Views

How to solve the equation $(1-e^{-αa})(1-e^{-βa}) = 1/2$ for a?

Published on 12 Apr 2026 - 1:38

List Question

Prove $\lim \limits_{h \to 0} \frac{a^h-1}{h} = \ln (a)$ without using L'hospital's.

Trouble with integration of following: $ \int^\infty_0 \exp(a(x)+b(x))a'(x)dx$

Is there a proof $e^ae^b=e^{a+b}$ using its power series expansion?

Simplifying an arbitrary constant.

Hints on solving $x^{2x}-(x^2+x)x^x+x^3=0$

How to solve $2^{\sin^2(x)}=\cos(x)$

Solving $|x-1|^{\log_2(4-x)} \le|x-1|^{\log_2 (1+x)}$

Exponential function using binomial approach and approximation by power series, both using python. Why different results?

A Series Representation for the Natural Logarithm Not Comprised of Exponential Terms

Finding the value of this exponential limit

Extension of a well known formula for the Euler number into the complex domain

Minimizing a function $f$ of the form $f(x)=\prod_if(x_i)$, is it possible to ensure $x_1,\ldots,x_j$ minimizes $\prod_i^jf(x_i)$?

Solving for i in mortgage payment formula in M = P [ i(1 + i)^n ] / [ (1 + i)^n – 1].

Inequality involving exponentials and integrals

How to solve the equation $(1-e^{-αa})(1-e^{-βa}) = 1/2$ for a?

Trending Questions

Popular # Hahtags

Popular Questions