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For any two complex numbers z1,z2 and any real numbers a a n d b , | a z 1 - b z 2 | 2 + | b z 1 + a z 2 | 2 = aa n db ,|a z_1-b z_2|^2+|b z_1+a z_2|^2=

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CENGAGE ENGLISH-LIMITS AND DERIVATIVES-All Questions
  1. Evaluate: ("lim")(xvecoo)x^3{sqrt(x^2+sqrt(1+x^4))-xsqrt(2)}

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  2. If m , n in N ,("lim")(xvec0)(sinx^n)/((sinx)^m)i s (a) 1, if n=m (b)...

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  3. For any two complex numbers z1,z2 and any real numbers <math xmlns="ht...

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  4. lim(n->oo)(-3n+(-1)^n)/(4n-(-1)^n) is equal to a. -3/4 b. 0 if n is...

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  5. Evaluate : ("lim")(xvecoo)(sqrt(25 x^2-3x)+5x)

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  6. Given a real-valued function f such that f(x)={(tan^2{x})/((x^2-[x]^2)...

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  7. Evaluate: lim(x-&gt;oo)((x^2+x-1)/(3x^2+2x+4))^((3x^2+x)/(x-2))

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  8. L=(lim)(x-&gt;a)(|2sinx-1|)/(2sinx-1)dotT h e n limit does not exis...

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  9. If [x] denotes the greatest integer less than or equal to x , then eva...

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  10. f(x)=("lim")(n-&gt;oo)x/(x^(2n)+1)dotT h e n , A. f(1^+)+f(1^(-1))...

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  11. Evaluate the limit: lim(x->1)((2x-3)(sqrt(x)-1))/(2x^2)

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  12. ("lim")(x->oo)sum(x=1)^(20)cos^(2n)(x-10) is equal to (a) 0 (b) 1 (...

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  13. lim(x-&gt;1) (1+sin((3pix)/(1+x^2)))/(1+cospix) is (a) 0 (b) 1 ...

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  14. f(x)=(1n(x^2+e^x))/(1n(x^4+e^(2x)))dotT h e n lim(x->oo)f(x) is equal...

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  15. ("lim")(n vec oo)"{"(n/(n+1))^(alpha)+sin (1/n)]^n(when alpha in Q) i...

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  16. The value of underset(xto2)lim(2^(x)+2^(3-x)-6)/(sqrt(2^(-x))-2^(1-x))...

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  17. If lim(n->oo)(n*3^n)/(n(x-2)^n +n*3^(n+1)-3^n) = 1/3 then the range of...

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  18. If ("lim")(x->a)[f(x)g(x)] exists, then both ("lim")(x->a)f(x)a n d("l...

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  19. If f(x)=lim(n->oo)n(x^(1/n)-1),then for x >0,y...

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  20. lim(n->oo)((n^2-n+1)/(n^2-n-1))^(n(n-1)) is

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