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The figure shows two regions in the firs...

The figure shows two regions in the first quadrant. `P(t, sin t^2) `the curve `B(t),A(t)` is the area under the curve `y = sin x^2` from `0` to `t` and `B(t)` is the area of the triangle with vertices ` P` and `M(t,0)`. Find `Lim _(t->0)A(t)/B(t)`

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ARIHANT MATHS-LIMITS-Exercise (Single Integer Answer Type Questions)
  1. The value of lim(n->oo)sum(k=1)^n(6^k)/((3^k-2^k)(3^(k+1)-2^(k+1)) is ...

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  2. The value of lim(xto (pi)/2) sqrt((tanx-sin{tan^(-1)(tanx)})/(tanx+cos...

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  3. The figure shows two regions in the first quadrant. P(t, sin t^2) the ...

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  4. If the two AB:(int(0)^(2t)((sinx)/x+1)dx)x+y=3t and AC:2tx+y=0 interse...

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  5. Consider a parabola y=(x^(2))/4 and the point F(0,1). Let A(1)(x(1),y...

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  6. If L=lim(xto(pi^(+))/2)(costan^(-1)(tanx))/(x-pi//2) then cos(2piL) is

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  7. Number of solutions of the equation cosectheta=k in [0,pi] where k=lim...

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  8. If C satisfies the equation lim(xto oo)((x+c)/(x-c))^(x)=4 then |(e^(c...

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  9. If lim(xto-oo)((3x^(4)+2x^(2)).sin(1/x)+|x|^(3)+5)/(|x|^(3)+|x^(2)|+|x...

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  10. If f(x)=lim(t to 0)[(2x)/(pi).tan^(-1)(x/(t^(2)))],then f(1) is …….

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  11. The value of lim(nto oo)(1/(sqrt(n^(2)))+1/(sqrt(n^(2)+1))+…..+1/(sqrt...

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  12. If l=lim(xto1^(+))2^(-2^(1/(1-x))) and m=lim(xto1^(+))(x sin (x-[x]))/...

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  13. The value of lim(xto 0)[(sinx.tanx)/(x^(2))] is …….. (where [.] deno...

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  14. If lim+(n to oo)sum(r=1)^(n)(kr)/(1xx3xx5xx….xx(2r-1)xx(2r+1))=1 then ...

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  15. If f(x)=lim(n to oo)sin^(4)x+1/4sin^(4)2x+..=1/(4^(n)).sin^(4)(2^(n)x)...

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  16. If f(x+y+z)=f(x)+f(y)+f(z) with f(1)=1 and f(2)=2 and x,y, z epsilonR ...

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  17. If lim(xto oo)(n.3^(n))/(n.(x-1)^(n)+n.3^(n+1)-3^(n))=1/3, the number ...

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  18. The value of lim(x->oo)(((x-1)(x-2)(x+3)(x+10)(x+15))^(1/5)-x) is .....

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  19. If lim(xto oo)([f(x)]+x^(2)){f(x)}=k, where f(x)=(tanx)/x and [.],{.} ...

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  20. The value of lim(ntooo){(sqrt(3)+1)^(2n)} is……..(where {.} denotes fra...

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