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lim(x->0)((1^x+2^x+...........+n^x)/n)^(...

`lim_(x->0)((1^x+2^x+...........+n^x)/n)^(1/x)` is equal to

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The value of lim_(xrarr0)(1^x+2^x+3^x+...+n^x)^(a//x)/n , is:

If lim_(xtoa)f(x)=1 and lim_(xtoa)g(x)=oo then lim_(xtoa){f(x)}^(g(x))=e^(lim_(xtoa)(f(x)-1)xg(x)) lim_(xto0)((x-1+cosx)/x)^(1/x) is equal to

lim_(xto0) ((2^(m)+x)^(1//m)-(2^(n)+x)^(1//n))/(x) is equal to

lim_(n->oo)n^2(x^(1/n)-x^(1/((n+1)))),x >0 , is equal to (a)0 (b) e^x (c) (log)_e x (d) none of these

lim_(x->0)(sin(x^2))/(1n(cos(2x^2-x))) is equal to (a) 2 (b) -2 (c) 1 (d) -1

lim_(x->0)(x^4(cot^4x-cot^2x+1)/(tan^4x-tan^2x+1)) is equal to (a) 1 (b) 0 (c) 2 (d) none of these

lim_(x->oo)(sin^4x-sin^2x+1)/(cos^4x-cos^2x+1) is equal to (a) 0 (b) 1 (c) 1/3 (d) 1/2

lim_(x->0) (Cosx -1)/x is equal to

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If lim_(xto0)(f(x))/(sin^(2)x)=8,lim_(xto0)(g(x))/(2cosx-xe^(x)+x^(3)+x-2)=lamda" and " lim_(x to 0)(1+2f(x))^((1)/(g(x)))=(1)/(e)," then" lim_(x to 0)(1+f(x))^((1)/(2g(x))) is equal to

CENGAGE PUBLICATION-LIMITS AND DERIVATIVES-All Questions
  1. Find the value of the limit ("lim")(xto0) (((sqrt(a+x))-(sqrt(a-x)))/...

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  2. Evaluate underset(xto0)lim(sin[cosx])/(1+[cosx]) ([.] denotes the grea...

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  3. lim(x->0)((1^x+2^x+...........+n^x)/n)^(1/x) is equal to

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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