I'm not very good with analysis (I never studied it) but because of my "work" on other topics of mathematics I came to this problem. lim_(k->+oo) log_k(k^a+k^b)=max(a,b) I'm sure that this is really "reasonable" because I tryed to graph it for really huge values of k ... but "reasonable" is not enough in mathematics: I'd like to prve this. So I'm courious to know how one should go to prove it in a formal way ... if it is true (I hope). PS: I know nothing about Limits and their rules

$\frac{20b}{{\left(4b^3\right)}^3}$

Which operation could we perform in order to find the number of milliseconds in a year??
${\displaystyle 60\cdot 60\cdot 24\cdot 7\cdot 365}$
${\displaystyle 1000\cdot 60\cdot 60\cdot 24\cdot 365}$
${\displaystyle 24\cdot 60\cdot 100\cdot 7\cdot 52}$
${\displaystyle 1000\cdot 60\cdot 24\cdot 7\cdot 52?}$

Tell about the meaning of Sxx and Sxy in simple linear regression,, especially the meaning of those formulas

Is the number 7356 divisible by 12? Also find the remainder.
A) No
B) 0
C) Yes
D) 6

What is a positive integer?

Determine the value of k if the remainder is 3 given ${\displaystyle (x^3+k{x}^2+x+5)÷(x+2)}$

Is $41$ a prime number?

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149600000000 is equal to
A)$1.496\times <!--\; \times \; -->{10}^{11}$
B)$1.496\times <!--\; \times \; -->{10}^{10}$
C)$1.496\times <!--\; \times \; -->{10}^{12}$
D)$1.496\times <!--\; \times \; -->{10}^8$

Find the value of$\log 1$ to the base $3$ ?

What is the square root of 3 divided by 2 .

write ${\displaystyle \sqrt[5]{{\left(7x\right)}^4}}$ as an equivalent expression using a fractional exponent.

simplify ${\displaystyle \sqrt{125n}}$

What is the square root of ${\displaystyle \frac{144}{169}}$