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If ("lim")(x->1)(2-x+a[x-1]+b[1+x]) exis...

If `("lim")_(x->1)(2-x+a[x-1]+b[1+x])` exists, then `a and b` can take the values of (where [.] denotes the greatest integer function). (a)`a=1/3,b=1` (b) `a=1, b=-1` (c) `a=9, b=-9` (d)`a=2, b=2/3`

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CENGAGE ENGLISH-LIMITS AND DERIVATIVES-All Questions
  1. Which of the following true ({.} denotes the fractional part of the ...

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  2. Evaluate: ("lim")(n->oo)(4^n+5^n)^(1/n)

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  3. If ("lim")(x->1)(2-x+a[x-1]+b[1+x]) exists, then a and b can take the ...

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  4. Evaluate: ("lim")(n→oo)(n^p sin^2(n !))/(n+1)

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  5. ("lim")(n→oo)(a n-(1+n^2)/(1+n))=b , where a is a finite number, then ...

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  6. Evaluate: ("lim")(xvecoo)x^3{sqrt(x^2+sqrt(1+x^4))-xsqrt(2)}

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

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

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

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

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

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

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

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

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

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

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

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

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

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