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If f(x)=underset(ntooo)limn(x^(1//n)-1),...

If `f(x)=underset(ntooo)limn(x^(1//n)-1)," then for "xgt0, ygt0,f(xy)` is equal to

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CENGAGE PUBLICATION-LIMITS AND DERIVATIVES-All Questions
  1. If underset(ntooo)lim(n.3^(n))/(n(x-2)^(n)+n.3^(n+1)-3^(n))=1/3, then ...

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  2. If ("lim")(xveca)[f(x)g(x)] exists, then both ("lim")(xveca)f(x)a n d(...

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  3. If f(x)=underset(ntooo)limn(x^(1//n)-1)," then for "xgt0, ygt0,f(xy) i...

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

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  5. underset(xto1)lim[cosec(pix)/(2)]^(1//(1-x)) (where [.] represents the...

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  6. Given lim(x to 0)(f(x))/(x^(2))=2, where [.] denotes the greatest inte...

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  7. Let f(x)=(x^2-9x+20)/(x-[x]) (where [x] is the greatest integer not gr...

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  8. Use formula lim(x->0)(a^x-1)/x=log(a) to find lim(x->0)(2^x-1)/((1+x)^...

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  9. Evaluate : lim(x to 0) {tan(pi/4+x)}^(1/x)

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  10. f(x) is the integral of (2sinx-sin2x)/(x^3),x!=0. Find lim(x->0)f^...

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  11. Evaluate underset (h to 0) lim ((a+h)^(2) sin (a+h) -a^(2) sin a)/h .

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  12. underset(xtooo)lim(x(logx)^(3))/(1+x+x^(2)) equals

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  13. underset(xto0)lim((2^(m)+x)^(1//m)-(2^(n)+x)^(1//n))/(x) is equal to

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  14. lim(x to 1) (1-x)tan((pix)/2)

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  15. If f(x)={sinx ,x!=npi,n in I2,ot h e r w i s e g(x)={x^2+1,x!=0,4,x=...

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  16. ("lim")(xvec0)[min(y^2-4y+11)(sinx)/x](w h e r e[dot]d e not e st h e ...

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  17. lim(x to pi/2)sin(xcosx)/("cos"(xsinx)) is equal to (a) 0 (b) pi/2 ...

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  18. If lim xto0(x^(-3)sin3x+a x^(-2)+b) exists and is equal to 0, then (a)...

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

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  20. lim(xto1) ((1-x)(1-x^(2))...(1-x^(2n)))/({(1-x)(1-x^(2))...(1-x^(n))}^...

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