Mathematics: Limit x~0 (√x+4)-2 x solve it in detail

Limit x~0 (√x+4)-2 x solve it in detail

Ответ:

LuisBanuelos000

10.03.2022

Rationalize the numerator:

$\dfrac{\sqrt{x+4}-2}x\cdot\dfrac{\sqrt{x+4}+2}{\sqrt{x+4}+2}=\dfrac{(\sqrt{x+4})^2-2^2}{x(\sqrt{x+4}+2)}=\dfrac x{x(\sqrt{x+4}+2)}=\dfrac1{\sqrt{x+4}+2}$

This is continuous at x=0 , so we can evaluate the limit directly by substitution:

$\displaystyle\lim_{x\to0}\frac{\sqrt{x+4}-2}x=\lim_{x\to0}\frac1{\sqrt{x+4}+2}=\frac1{\sqrt4+2}=\frac14$

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Ответ:

Gocu5076

26.03.2020

Mathematics

see #7 below

Step-by-step explanation:

$\begin{array}{lcl}\underline{\quad \text{ Statement}\quad }&&\underline{\quad \text{Reason}\quad}\\1.\ DE||AC&&1.\ Given\\2.\ AB\ is\ a\ transversal&&2.\ Conclusion\ from\ Statement\ 1\\3.\ &&3.\ \\4.\ \angle B=\angle B&&4.\ Reflexive\ Property\ of\ Equality\\5.\ &&5.\ \\6.\ \dfrac{BD}{BA}=\dfrac{BE}{BC}&&6.\ Converse\ of\ SSS\ Similarity\ Thm\\\end{array}$

7. ΔABC ≅ ΔDBC 7. SAS Similarity Theorem

A much easier way to prove these triangles are similar is to add either #3 or #5:

Statement Reason

3. ∠A ≡ ∠D 3. Corresponding Angles Postulate

5. ∠C ≡ ∠E 5. Corresponding Angles Postulate

to prove

7. ΔABC ≅ ΔDBC 7. AA Similarity Theorem

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Limit x~0 (√x+4)-2 x solve it in detail

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