11 - Limit Continuity and Differentiability Questions Answers

sir pls provide detailed solution asap
Asked By: HARDIK
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Find 

lim nā†’āˆž  āæāˆš(n!) / n

Asked By: LUFFY
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Joshi sir comment

Sir , i have solved   limx-->0    (sin-1x  - tan-1x )/x. plz have a look on others.

Asked By: VISHAL PHOGAT
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Joshi sir comment

limx-->0    (sin-1x  - tan-1x )/x3

use D L Hospital rule or expansion of sin-1x and tan-1x to solve it

no of solutions of  e-x^2/2 - x2 = 0 are

Asked By: VISHAL PHOGAT
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Joshi sir comment

two intersecting points means two solutions

lim x»infinity( ((x+1)(x+2)(x+3)(x+4))^¼ - x )

Asked By: VISHAL PHOGAT
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Joshi sir comment

multiply with the conjugate in numerator again and again you will get 

limx->((x+1)(x+2)(x+3)(x+4) - x4)/((x+1)(x+2)(x+3)(x+4))1/4 + x )*((x+1)(x+2)(x+3)(x+4))1/2 + x2 )

after solving the numerator get a 3 power expression of x then take 3 power of x common, similarly take x and 2 power of x from the first and second denominator terms

lim n--> ∞  4^n/n!

Asked By: HIMANSHU MITTAL
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Joshi sir comment

limn->∞ 4n/ n!

= limn->∞ [4/1][4/2][4/3][4/4][4/5][4/6][4/7]................................[4/n]

besides first four bracket, all brackets are real numbers less than 1 so their product will be zero for n tends to infinite

 

 

 

 

 

Importance High!!!!!!!!!!!!!!!!!

 

Dear Sir / Madam

 

Myself Rajeev Shrivastava, I am putting a signs series in front of you which based on numbers from 01 to 100. Actually I want to know that what reason of behind Approx equability of signs is 

(++), (+-), (--) & (-+) at end of the month or year between the below mentioned.

 

Let's define a kind of mapping:
0↔1
2↔3
4↔5
6↔7
8↔9

(+) means: an Even number
(-) means: an Odd number

I simply say: for any EO (+-) it exists an OE (-+) which is paired to.
And that's true since each E is mapped to a O and vice versa (1 to 1 relation where "f(f(x))=x" ) !
E.g.: 29 ↔ 83

There is 25 numbers in the EO (+-) group, so 25 in OE (+-).
There is 25 numbers in the EE (++) group, so 25 in OO (--).

Picking a number at random between 01 and 100 inclusive is choosing equitably in EO, OE, EE or OO group. (25% for each)

 

So, I really need of your help to solve a puzzle please. I just am trying to make you understand what type of solution I need:

 

There are some results for your review:

MONTH

DATE

DAY

FIRST_SERIES

SECOND_SERIES

FIRST_SERIES

SECOND_SERIES

APR

1

SUN

+

-

-

+

+-

-+

APR

2

MON

+

+

-

+

++

-+

APR

3

TUE

+

-

+

-

+-

+-

APR

4

WED

+

+

+

+

++

++

APR

5

THU

-

+

-

+

-+

-+

APR

6

FRI

+

+

+

-

++

+-

APR

7

SAT

+

-

-

+

+-

-+

APR

8

SUN

-

+

+

-

-+

+-

APR

9

MON

-

+

-

+

-+

-+

APR

10

TUE

+

+

+

+

++

++

APR

11

WED

+

+

-

-

++

--

APR

12

THU

-

+

-

-

-+

--

APR

13

FRI

+

+

+

+

++

++

APR

14

SAT

+

-

+

-

+-

+-

APR

15

SUN

+

-

+

-

+-

+-

APR

16

MON

-

-

+

+

--

++

APR

17

TUE

-

-

+

+

--

++

APR

18

WED

 

 

 

 

 

 

APR

19

 THU

 

 

 

 

 

 

APR

20

 FRI

 

 

 

 

 

 

APR

21

 SAT

 

 

 

 

 

 

APR

22

 

 

 

 

 

 

 

APR

23

 

 

 

 

 

 

 

 

  (Complete sheets for the year 2011 and 2012 are attached with this mail)

 

You can see that there are two times falls in a day of pair make by even (+) and odd (-) signs, i.e. (++), (+-), (--) & (-+) as above said.

The total of pair combination signs become approx equal to each other at the end of the month or year (every year- so, I am sending you attachment to go through the year’s result).

By this analysis:

1-     I want to know that what is the relation between current falling signs and past fell signs.

2-     How can I come to know, what type of combination of sign would be any particular date or day.

3-     As you can seen on 22nd and 23rd April’2012 I don’t know what combination of sign is.

4-     There is surety that there is some relation between current First fall of combination of signs and past fall or First fall of combination of signs and Second fall of combination of signs.

 

Please help me to how come to know what type of fall may be for next day by reviewing past or first combination of signs. So reply or elaborate me with an example.

 

 I would be very grateful to you till entire life.

 

Regards

 

RAJEEV SHRIVASTAVA

 

 

 

Importance High!!!!!!!!!!!!!!!!!

 

Dear Sir / Madam

 

Myself Rajeev Shrivastava, I am putting a signs series in front of you which based on numbers from 01 to 100. Actually I want to know that what reason of behind Approx equability of signs is 

(++), (+-), (--) & (-+) at end of the month or year between the below mentioned.

 

Let's define a kind of mapping:
0↔1
2↔3
4↔5
6↔7
8↔9

(+) means: an Even number
(-) means: an Odd number

I simply say: for any EO (+-) it exists an OE (-+) which is paired to.
And that's true since each E is mapped to a O and vice versa (1 to 1 relation where "f(f(x))=x" ) !
E.g.: 29 ↔ 83

There is 25 numbers in the EO (+-) group, so 25 in OE (+-).
There is 25 numbers in the EE (++) group, so 25 in OO (--).

Picking a number at random between 01 and 100 inclusive is choosing equitably in EO, OE, EE or OO group. (25% for each)

 

So, I really need of your help to solve a puzzle please. I just am trying to make you understand what type of solution I need:

 

There are some results for your review:

MONTH

DATE

DAY

FIRST_SERIES

SECOND_SERIES

FIRST_SERIES

SECOND_SERIES

APR

1

SUN

+

-

-

+

+-

-+

APR

2

MON

+

+

-

+

++

-+

APR

3

TUE

+

-

+

-

+-

+-

APR

4

WED

+

+

+

+

++

++

APR

5

THU

-

+

-

+

-+

-+

APR

6

FRI

+

+

+

-

++

+-

APR

7

SAT

+

-

-

+

+-

-+

APR

8

SUN

-

+

+

-

-+

+-

APR

9

MON

-

+

-

+

-+

-+

APR

10

TUE

+

+

+

+

++

++

APR

11

WED

+

+

-

-

++

--

APR

12

THU

-

+

-

-

-+

--

APR

13

FRI

+

+

+

+

++

++

APR

14

SAT

+

-

+

-

+-

+-

APR

15

SUN

+

-

+

-

+-

+-

APR

16

MON

-

-

+

+

--

++

APR

17

TUE

-

-

+

+

--

++

APR

18

WED

 

 

 

 

 

 

APR

19

 THU

 

 

 

 

 

 

APR

20

 FRI

 

 

 

 

 

 

APR

21

 SAT

 

 

 

 

 

 

APR

22

 

 

 

 

 

 

 

APR

23

 

 

 

 

 

 

 

 

  (Complete sheets for the year 2011 and 2012 are attached with this mail)

 

You can see that there are two times falls in a day of pair make by even (+) and odd (-) signs, i.e. (++), (+-), (--) & (-+) as above said.

The total of pair combination signs become approx equal to each other at the end of the month or year (every year- so, I am sending you attachment to go through the year’s result).

By this analysis:

1-     I want to know that what is the relation between current falling signs and past fell signs.

2-     How can I come to know, what type of combination of sign would be any particular date or day.

3-     As you can seen on 22nd and 23rd April’2012 I don’t know what combination of sign is.

4-     There is surety that there is some relation between current First fall of combination of signs and past fall or First fall of combination of signs and Second fall of combination of signs.

 

Please help me to how come to know what type of fall may be for next day by reviewing past or first combination of signs. So reply or elaborate me with an example.

 

 I would be very grateful to you till entire life.

 

Regards

 

RAJEEV SHRIVASTAVA

 
Asked By: RAJEEV SHRIVASTAVA
is this question helpfull: 8 1 read solutions ( 1 ) | submit your answer
Joshi sir comment

If you are making the sequence on the basis of dates then you should take signs accordingly then you can make this sequence for many years

for example if you take 23 june then first sign series will be +-, + for even number and - for odd number , now as conversion rule as you gave in your explanation 23 will be converted to 32 so second series will be -+

similarly you can make it for any date 

for example 29 december first series will be +- and its conversion is 38 so next series will be -+

if you are thinking something else then explain your question correctly 

ABC is an isosceles triangle inscribed in a circle of radius r. If  AB=AC and h is the altitude from A to BC. and P and φ denote the perimeter and area of the triangle respectively, then  lim n−» 0   φ/p³ is equal to??

Asked By: AMIT DAS
is this question helpfull: 8 0 submit your answer
Joshi sir comment

 

first draw a cirle and triange inside it , consider angle B and angle C asα so angle A = 180-2α, let centre of the circle is O and D is the point in the line BC where altitude meets in the line BC, given that altitude = h and radius = r

so AB = AC = h cosecα and BC = 2 h cotα so 

p = 2 h (cosecα + cotα)

and φ = 1/2  2 h cotα h = h2 cotαa

and in triangle OBD angle OBD = 2α - 90    so cos(2α - 90) = h cotα /r   implies that h = 2 r sin2α 

now i think limit will be based on h not n

 lim h−» 0   φ/p³  = 1/128r

for getting solution put p and φ first then put h in terms of r, you will get an equation based on α and r,

convert limh->0  to  limα->0     because when h will be 0, α will also be 0 

 

limit  n tends to ∞

then

(x^n)/(n!) equals

Asked By: AMIT DAS
is this question helpfull: 5 0 submit your answer
Joshi sir comment

let y = lim n->∞ (xn/n!)

or y = x lim n->∞ (1/n) lim n->∞ xn-1/(n-1)!

or y = 0

 

limit n tends to ∞

x{ [tan‾¹ (x+1/x+4)] - (π/4)}

Asked By: AMIT DAS
is this question helpfull: 6 0 submit your answer
Joshi sir comment

 

I think n is printed by mistake, so considering it as x

the question will be limit x tends to ∞

x{ [tan-1 (x+1/x+4)] - (π/4)}

consider [tan-1 (x+1/x+4)] - (π/4) = θ

so [tan-1 (x+1/x+4)] = (π/4)+θ

so (x+1/x+4) = tan(π/4+θ)

or x = (-3-5tanθ)/2tanθ

so converted question will be limθ->0  (-3-5tanθ)θ/2tanθ

solve

Solution by Joshi sir

 

I think n is printed by mistake, so considering it as x

the question will be limit x tends to ∞

x{ [tan-1 (x+1/x+4)] - (π/4)}

consider [tan-1 (x+1/x+4)] - (π/4) = θ

so [tan-1 (x+1/x+4)] = (π/4)+θ

so (x+1/x+4) = tan(π/4+θ)

or x = (-3-5tanθ)/2tanθ

so converted question will be limθ->0  (-3-5tanθ)θ/2tanθ

now we know that limθ->0 tanθ/θ = limθ->0 θ/tanθ = 1

so next line will be limθ->0 (-3-5tanθ)/2 = -3/2 

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