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Submit By: MANISH SIR 5 year ago
is this topic helpfull: 20 5

if f(X)=xlxl then find f-1(x) can you please explain me the meaning and use of sgn

 

Asked By: NIKHIL VARSHNEY 7 year ago
is this question helpfull: 18 2 submit your answer
Answer Strategies and trick by Manish sir (it will help you to solve it by yourself)

f(x) = x|x|  => f(x) = -x2  for negative real values of x  and f(x) = x2 for positive real values of x

so f-1(x) = -√|x|  for negative real values and = +√|x| for positive real values of x

 

The number of real negative terms in the binomial expansion of (1+ix)(4n-2),  n  N and x > 0 is?

Asked By: KAMAL 7 year ago
is this question helpfull: 6 0 read solutions ( 1 ) | submit your answer
Answer Strategies and trick by Manish sir (it will help you to solve it by yourself)

Total number of terms in the expansion = 4n-2+1 = 4n-1

for a negative real number i2 is compulsory so associated terms are 3rd, 7th, 11th ..........

Total number of terms = n

which of the following is differntiable at x=0 ?

cos(lxl)+lxl

sin(lxl)-lxl

Asked By: NIKHIL VARSHNEY 7 year ago
is this question helpfull: 11 3 submit your answer
Answer Strategies and trick by Manish sir (it will help you to solve it by yourself)

sin(|x|)+|x| is differentiable at x = 0

LHD of first = {cos|0+h|+|0+h|-cos|0|-|0|}/0+h-0  = (cosh+h-1)/h = (1-2sin2h+h-1)/h = 1 (on taking limits)

now check RHD, its value will be -1

similarly in second both values are 0 so it is differentiable

blushblushConsider a branch of the hyperbola  x²-2y²-2√2x-4√2y-6=0, with vertex at the point A. Let B be one of the end points of its latus rectum .If C is the focus of the hyperbola nearest to the point A, then the area of the triangle ABC is ??????smiley

Asked By: AMIT DAS 7 year ago
is this question helpfull: 6 0 submit your answer
Answer Strategies and trick by Manish sir (it will help you to solve it by yourself)

 

x²-2y²-2√2x-4√2y-6=0 

Arrange this equation in form of standard hyperbola as 

(x-√2)2/4 - (y+√2)2/2 = 1

so X = x-√2, Y = y+√2

vertex coordinate :  X = 0 and Y = 0 so x = √2, y = -√2

similarly focus : X = ae, Y = 0,     here a = 2, b = √2 and b2 = a2(1-e2)

and end point of latus rectum : X = ae, Y = b2/a

solve the area and get the answer

 

 

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