Common factors of 60,36,48

CALC- limits please show your method

gladu [14]

A. Factor the numerator as a difference of squares:

$\displaystyle\lim_{x\to9}\frac{x-9}{\sqrt x-3}=\lim_{x\to9}\frac{(\sqrt x-3)(\sqrt x+3)}{\sqrt x-3}=\lim_{x\to9}(\sqrt x+3)=6$

c. As $x\to\infty$ , the contribution of the terms of degree less than 2 becomes negligible, which means we can write

$\displaystyle\lim_{x\to\infty}\frac{4x^2-4x-8}{x^2-9}=\lim_{x\to\infty}\frac{4x^2}{x^2}=\lim_{x\to\infty}4=4$

e. Let's first rewrite the root terms with rational exponents:

$\displaystyle\lim_{x\to1}\frac{\sqrt[3]x-x}{\sqrt x-x}=\lim_{x\to1}\frac{x^{1/3}-x}{x^{1/2}-x}$

Next we rationalize the numerator and denominator. We do so by recalling

$(a-b)(a+b)=a^2-b^2$
$(a-b)(a^2+ab+b^2)=a^3-b^3$

In particular,

$(x^{1/3}-x)(x^{2/3}+x^{4/3}+x^2)=x-x^3$
$(x^{1/2}-x)(x^{1/2}+x)=x-x^2$

so we have

$\displaystyle\lim_{x\to1}\frac{x^{1/3}-x}{x^{1/2}-x}\cdot\frac{x^{2/3}+x^{4/3}+x^2}{x^{2/3}+x^{4/3}+x^2}\cdot\frac{x^{1/2}+x}{x^{1/2}+x}=\lim_{x\to1}\frac{x-x^3}{x-x^2}\cdot\frac{x^{1/2}+x}{x^{2/3}+x^{4/3}+x^2}$

For $x\neq0$ and $x\neq1$ , we can simplify the first term:

$\dfrac{x-x^3}{x-x^2}=\dfrac{x(1-x^2)}{x(1-x)}=\dfrac{x(1-x)(1+x)}{x(1-x)}=1+x$

So our limit becomes

$\displaystyle\lim_{x\to1}\frac{(1+x)(x^{1/2}+x)}{x^{2/3}+x^{4/3}+x^2}=\frac{(1+1)(1+1)}{1+1+1}=\frac43$

3 0

3 years ago

-3x + 22 greater than equal to -5

melamori03 [73]

Answer:

x is less than or equal to 9

which is x ≤ 9

Step-by-step explanation:

8 0

2 years ago

What is 247,039 rounded to the nearest thousand

DerKrebs [107]

Answer:
247,000

Explanation:
To round a number to the nearest thousand, we check the digit in the hundreds position:
1- If the digit is less than 5, then we round down. This means that we simply convert all digits after the thousands to zero and that's it
2- If the digit is equal to or more than 5, then we round up. This means that we add one to the thousands digit and then convert all digits after the thousands to zero.

In the given number 247039, the number in the hundreds position is 0. This means that we will round down

Therefore, 246039 rounded to the nearest thousand would simply give 247000

Hope this helps :)

6 0

3 years ago

Is

rjkz [21]

Answer:

It is the first answer choice.

Step-by-step explanation.

Use synthetic division and there is no remainder, so -1 is a factor

5 0

2 years ago

Which angle measure is the measure of an obtuse angle? 90° 64° 105° 87°

fenix001 [56]

Answer:

105°

Step-by-step explanation:

6 0

3 years ago

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