59 - Calculus Questions Answers

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

Maths >> Calculus >> Functions IIT JEE

 best calculus books for iitjee.

Asked By: KRISHN RAJ
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Joshi sir comment

its I. E. Maron 

 

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

 

Sir,is the function (2x+5) is differentiable everywhere in its domain set. If yes the what is the case with l2x+5l.
Asked By: GAURAV MAHATE
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Joshi sir comment

since first one is a straight line so at every point only one tangent is possible so it is differentiable

but second one which is modulus has a sharp turn at x = -5/2 so two tangents at x = -5/2 are possible so is not differentiable.

A window frame is shaped like a rectangle with an arch forming the top ( ie; a box with a semicircle on the top)

The vertical straight side is Y, the width at the base and at the widest part of the arch (Diam) is X.

I know that the perimeter is 4.

Find X if the area of the frame is at a maximum?

Asked By: ROBERT DEPANGHER
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Joshi sir comment

perimeter = 4 so 2Y + X + πX/2 = 4

and area = XY + [π(X/2)2]/2

put Y from 1st equation to 2nd we get A = X[4-X{1+(π/2)}]/2 + πX2/8

now calculate dA/dX and then compare it to zero

X will be 8/(4+π)

y=px+a/p

Asked By: FRANCISBHORGIA
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Joshi sir comment

this is a special type of differential equation in which p = dy/dx

its solution will be y = cx+(a/c)  here c is a constant

y-xp=x+yp

Asked By: FRANCISBHORGIA
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Joshi sir comment

on applying p = dy/dx

(ydx-xdy)/dx = (xdx+ydy)/dx

or ydx-xdy = xdx+ydy

or dy/dx = (y-x)/(y+x)

now it is homogeneous

 

 

 

 

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 

how to find differential eqn. of all conics whose axes coincide with coordinate axes??   tell me the eqn. of tht. conic

Asked By: SHALINI SINGH
is this question helpfull: 10 4 submit your answer
Joshi sir comment

Parabola   eq.  y2 = 4ax ,

on differentiating this eq. with respect to x we get 2y(dy/dx) = 4a                        

on taking this value of 4a in eq. y2= 4ax we will get the differential eq. of parabola.

similarly for ellipse    x2/a2  +   y2/b2  =   1

on differentiaing this eq. twice we will get two additional eq. 

by solving these eq. get an eq. free from a and b, this will be the differential eq. of the ellipse.

similarly for hyperbola

 

 

 

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