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If F(t)=int(x+y)dt then the value of F(p...

If `F(t)=int(x+y)dt` then the value of `F(pi/2)-F(0)` is 1 (b) `-1` (c) `e^(pi//2)` (d) 0

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BANSAL-LIMITS AND DERIVATIVES-All Questions
  1. If y=1/(1+x^(n-m)+x^(p-m))+1/(1+x^(m-n)+x^(p-n))+1/(1+x^(m-p)+x^(n-p))...

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  2. A curve is represented parametrically by the equations x = e^t cos t a...

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  3. If F(t)=int(x+y)dt then the value of F(pi/2)-F(0) is 1 (b) -1 (...

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  4. If 2^x+2^y=2^(x+y) then (dy)/(dx)

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  5. Two functions f & g have first & second derivatives at x=0 & satisfy t...

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  6. Let P(x) be the polynomial x^3+a x^2+b x+c , where a ,\ b ,\ c in R ....

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  7. If sqrt(y+x)+sqrt(y-x)=c (where c!=0 ), then dy/dx

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  8. For the function y=f(x)=(x^2+b x+c)e^x , which of the following holds?...

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  9. Let f'(x)=3x^2sin1/x-xcos1/x , if x!=0\ ; f(0)=0 and f(1//pi)=0 then: ...

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  10. If f(x)=xdot|x|, then its derivative is : (a)2x (b) -2x (c) 2|x|...

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  11. Find derivative of u(x) u( x )= [ ln( 1+ sin2x ), if x>0 ...

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  12. find v( x )= Lim t→0 2x/ π tan −1 ( 2 /t )

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  13. ("Lim")(n->oo)((1+tanpi/(2n))/(1+sinpi/(3n)))^n equal

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  14. ("Lim")(x->0^+)1/((1+"c o s e c"x)^(1/(ln(sinx)))) equals

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  15. ("Lim")(x->0)(2/picos^(-1)x)^(1//x) equals

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  16. Evaluate: intsqrt((1-sin2x)/(1+sin2x))dx

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  17. Find the differentiation of ((cot^2x-1)/(cot^2x+1)) w.r.t. \ x

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  18. Find the differentiation of sqrt(sec^2x+"c o s e c"^2x) w.r.t. \ x

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  19. Find the differentiation of (1+x^(1/4))(1+x^(1/2))(1-x^(1/4)) w.r.t. \...

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  20. Find the differentiation of (log)(sqrt(x))(1/x) w.r.t. \ x

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