Question

Hey I will be posting all question on Limits by AK Sanyal(Maths teacher) any of you who can solve any of them will have my appreciation

Answer 1

this site is more designed for interactions that promote studying as opposed to simply giving our free answers ... just a public service announcement :)

Answer 2

but feel free to tickle our fancies with something more stimulating than finding the slope between 2 points :)

Answer 3

\[\lim_{x \rightarrow 2}\left( (12/(8-x ^{3}) )-(1/(2-x))\right)\]
\[\lim_{x \rightarrow 0} \left(\ln (\cos x+\sin x)/(\sqrt{3+2x}-\sqrt{3-7x}) \right) \]
\[\lim_{x \rightarrow 3}\left( (\sqrt{x}-\sqrt{3}+\sqrt{x-3})/\sqrt{x ^{2}-9} \right)\]
\[\lim_{x \rightarrow \beta}\left( (1-\cos (ax ^{2}+bx+c))/(\beta-x)^{2} \right)\] where \[\alpha\] and \[\beta\] are roots of \[ax ^{2}+bx+c=0\]

Answer 4

feel free to solve them theese are just 4 out 34 such questions

Answer 5

for ease of reading: \frac{top}{bottom} formats to:\[\frac{top}{bottom}\]

Answer 6

\[\lim_{x \to 3}\frac{\sqrt{x}-\sqrt{3}+\sqrt{x-3}}{\sqrt{x ^{2}-9}}\]

Answer 7

this style is much better thank you but how do you find it in the equations panel

Answer 8

since this goes to 0/0 we can most likely Lhop it

Answer 9

\[\frac{\top}{bottom}\] just by typing it in; but apparently it reads top is a special word lol

Answer 10

you can type it directly into the reply box as well; which is what most of us become used to

Answer 11

In the first one ... 8-x^3 can be written as (2-x)(4+ x^2 + 2x)

Now take LCM. We get [ 12- 4 - x^2 - 2x] / (2-x)( 4+ x^2 + 2x)

by factorising we get... [ (x+4) ( 2-x) ] / [ (2-x)(4 + x^2 +2x)]

2-x gets cancelled. we are left with (x+4) . now put x=2. we get the value 6.

Answer 12

conjugates onthe other hand tend to be your friend whin you got sqrts underneath

Answer 13

in this case tho I think they might not help hmm

are you familiar with using Lhopitals rule?

Answer 14

me? yes. I am familiar with Lhospital's rule.

Answer 15

that was more directed at the asker tho, but you know; its fair game lol

Answer 16

http://www.wolframalpha.com/input/?i=limit+x+to+3+%28sqrt%28x%29-sqrt%283%29%2Bsqrt%28x-3%29%29%2F%28sqrt%28x%5E2-9%29%29

1/sqrt(6) but i got no idea how they did it; it should be in the show steps part tho

Answer 17

For last is the answer (2beta + b )^2 / 2beta