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If lim(xto0)(x^n-sinx^n)/(x-sin^n x) is ...

If `lim_(xto0)(x^n-sinx^n)/(x-sin^n x)` is non-zero finite, then `n` must be equal to 4 (b) 1 (c) 2 (d) 3

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CENGAGE PUBLICATION-LIMITS AND DERIVATIVES-All Questions
  1. lim(x->0)((1^x+2^x+...........+n^x)/n)^(1/x) is equal to

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  2. Consider the following graph of the function y=f(x). Which of the foll...

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  3. If lim(xto0)(x^n-sinx^n)/(x-sin^n x) is non-zero finite, then n must b...

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  4. If underset(xtoa)lim[f(x)+g(x)]=2 and underset(xtoa)lim[f(x)-g(x)]=1, ...

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  5. Among (i) underset(xtooo)limsec^(-1)((x)/(sinx))" and "(ii) underset(x...

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  6. Evaluate lim(x->0)(3x+|x|)/(7x-5|x|)

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  7. The value of lim(x->0)(1+sinx-cosx+"log"(1-x))/(x^3) is (a)1/2 ...

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  8. f(x)={x ,xlt=0 1,x=0,t h e nfin d("lim")(xvec0)f(x)x^2,x >0ife xi s t ...

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  9. underset(xtooo)lim(e^(1//x^(2))-1)/(2tan^(-1)(x^(2))-pi) is equal to

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  10. Evaluate: lim(x->oo) (1+1/(a+bx))^(c+dx) , where a,b,c and dare positi...

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  11. If x1=3 and x(n+1)=sqrt(2+xn),ngeq1,t h e n""("lim")(xrarroo)xn is (...

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  12. Evaluate: ("lim")(xtooo) (1+1/x)^x

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  13. lim(x->0)("cos"(tanx)-cosx)/(x^4)i se q u a lto 1/6 (b) -1/3 (c) 1/...

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  14. Evaluate: ("lim")(xrarr0)((a^x+b^x+c^x)/3)^(2/x);(a , b , c >0)

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  15. underset(xtooo)lim{(x+5)tan^(-1)(x+5)-(x+1)tan^(-1)(x+1)} is equal to

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  16. If f(n)=underset(xto0)lim{(1+"sin"(x)/(2))(1+"sin"(x)/(2^(2)))...(1+"s...

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  17. If underset(xto-2^(-))lim(ae^(1//|x+2|)-1)/(2-e^(1//|x+2|))=underset(x...

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  18. The population of a country increases by 2% every year. If it increase...

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  19. Evaluate lim(xto-oo)[(x^(4)sin((1)/(x))+x^(2))/((1+|x|^(3)))].

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  20. Evaluate the limit: lim(x->oo)((x+2)/(x+1))^(x+3)

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