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T1 is an isosceles triangle in circle C...

`T_1` is an isosceles triangle in circle C. Let `T_2` be another ísosceles triangle inscribed in C whose base is one of the equal sides of `T_1` and which overlaps the interior of `T_1`. Similarly, create isosceles triangle `T_3` from `T_2; T_4 and T_5`, and so on. Prove that the triangle `T_n`, approaches an equilateral triangle as `n ->oo`,

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CENGAGE ENGLISH-LIMITS AND DERIVATIVES-All Questions
  1. If f(x)=(cosx)/((1-sinx)^(1/3)) then (a) ("lim")(xrarrpi/2)f(x)=-oo (b...

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  2. lim(x->-oo)(x^2*tan(1/x))/(sqrt(8x^2+7x+1)) is

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  3. T1 is an isosceles triangle in circle C. Let T2 be another ísoscele...

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  4. If f(x)=0 is a quadratic equation such that f(-pi)=f(pi)=0 and f(pi/2)...

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  5. ("lim")(xvecoo)[(e/(1-e))(1/e-x/(1+x))]^xi s e^((1-e)) (b) e^(((1-e)...

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  6. ("lim")(x -> 0)((1+tanx)/(1+sinx))^(cos e cx) is equal to (a)e (b...

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  7. ("lim")(xvecoo)(sin^4x-sin^2x+1)/(cos^4x-cos^2x+1) is equal to (a) ...

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  8. Find (dy)/(dx) if y=tan^(-1)((4x)/(1+5x^2))+tan^(-1)((2+3x)/(3-2x))

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  9. "F i n d"(dy)/(dx)"if"y=tan^(-1)((sqrt(1+x^2)-1)/x), where x!=0

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  10. If y=sin^(-1)((2x)/(1+x^2)), then find (dy)/(dx)

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  11. If y=tan^(-1)((3x-x^3)/(1-3x^2)),-1/(sqrt(3))ltxlt1 /(sqrt(3)), then f...

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  12. Find (dy)/(dx) for the functions: y=(x+sinx)/(x+cosx)

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  13. Find the derivative of the function given by f(x)=(1+x)(1+x^2)(1+x^4)(...

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  14. Find (dy)/(dx) if y=sec^(-1)((sqrt(x)+1)/(sqrt(x)-1))+sin^(-1)((sqrt(x...

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  15. Let f(x)=xsinpix ,x > 0. Then for all natural numbers n ,f^(prime)(x) ...

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  16. Find (dy)/(dx) if y=tan^(-1)((4x)/(1+5x^2))+tan^(-1)((2+3x)/(3-2x))

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  17. If y=sec^(-1)(1/(2x^2-1));0ltxlt (sqrt(2)),="" then="" find="" (dy)/(d...

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  18. (d^2x)/(dy^2) equals: (1) ((d^2y)/(dx^2))^-1 (2) -((d^2y)/(dx^2))^-1...

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  19. Find (dy)/(dx) if y=log{e^x((x-2)/(x+2))^(3/4)}

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  20. let f(x)=2+cosx for all real x Statement 1: For each real t, there ex...

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