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                   if f:R->[pi/6,pi/2),f(x)= arcsin (x^2 - a/x^2 + 1) is a onto function,den set of values of "a" is.....


3 years ago

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                                        Ans:$y = sin^{-1}(x^{2}-\frac{a}{x^{2}}+1)$$(x^{2}-\frac{a}{x^{2}}+1)=siny$$x^{4}+(1-siny)x^{2}-a=0$This is simple Quadratic in x2,$\Delta \geq 0$$(1-siny)^{2}\geq 4.(-a)$$sin^{2}y-2siny+1+4a\geq 0$$\Delta <0$$4<4(4a+1)$$a>0$Thanks & RegardsJitender SinghIIT DelhiaskIITians Faculty

one year ago

Image attached ….....

 Jitender Singh one year ago

Sir explain this solution. I n = d n-1 /dx n-1 [x n-1 + nx n-1 log x ] In = (n-1) d n-2 / dx n-2 x n-2 + n d n-1 / dx n-1 (x n-1 logx) I n = (n-1 ) ! + nI n-1 In – nI n-1 =(n-1)! Proved

 milind one year ago
What could be the best book for doing problems on limits and continuity?

That would depend on whether you are, preparing for CBSE subjective questions or competetive exam questions. In context of the former, R.S. Agarwal, R. D. Sharma or other substitutes to them...

 Ravi 9 months ago

amit m aggarwal by arihant series is the best for calculus(entire series for differential and integral)both are separate books solutions are also provided in the same book itself for iit...

 vineet chatterjee 9 months ago
I made a circle in attachment …. .here theta = cos-1 x ...Lekin usne fir bhi theta ki value nhi rakhi ….wo theta ki value rakh ke bhi to x ke respect differential kar sakta tha …..please...

GIVEN QUESTION IS TO BE SOLVED USING THE CONCEPT OF PARMETRIC EQUATIONS.IF HE WOULD HAVE PLACED THE VALUE OF THETA AS cos-1x THE SOLUTION WOULD HAVE BECAME MUCH MORE COMPLICATED BUT THE...

 siddharth gupta one year ago

No siddharth answer is not same check it bro

 milind one year ago

If anybody there then help

 milind one year ago
Q . PLEASE INTEGRATE THE FUNCTION WHOSE PIC IS ATTACHED.....

divide num and denom. by x^2, then substitute ax + b/x = t.

 Nihal Raj 10 months ago

divide num and denom. by x^2, then substitute ax + b/x = t.

 Nihal Raj 10 months ago

thanks

 Bharat Makkar 10 months ago
(cot 2 a (sec a – 1))/1 + sin a = sec 2 a( 1 – sin a)/(1 + sec a)

write cot 2 a = cos 2 a/sin 2 a = (1-sin 2 a)/(1-cos 2 a) = (1+sin a)(1-sin a) / (1+cos a)(1-cos a). Put cos a = 1/sec a. cot 2 a = (1+sin a)(1- sin a)*sec 2 a/(sec a+1)*(sec a – 1). Put...

 Akshay one month ago
Q . EQUATION OF THE STRAIGHT LINE BELONGING TO THE FAMILY OF LINES :- ( x + y ) + k( 2x – y +1) =0 , THAT IS FARTHEST FROM ( 1 , – 3) IS :- 13y – 6x = 7 13y + 6x = 0 15y + 6x =7 15y – 6x = 7

The point of intersection of given family of lines is the point of intersection of x+y=0 and 2x-y+1=0 and it is (-1/3 1/3). The required line belongs to the given family so it must pass...

 Himaja 8 months ago

thanks....got it

 Bharat Makkar 8 months ago
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