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If ("lim")(x->a)[f(x)g(x)] exists, then ...

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

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CENGAGE ENGLISH-LIMITS AND DERIVATIVES-All Questions
  1. The value of underset(xto2)lim(2^(x)+2^(3-x)-6)/(sqrt(2^(-x))-2^(1-x))...

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

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

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

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  6. ("lim")(x->1)[cos e c(pix)/2]^(1/((1-x))) (w h e r e [dot] represents ...

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  7. Given ("lim")(xvec0)(f(x))/(x^2)=2, \where\ [dot] denotes the greatest...

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

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  9. 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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  10. Find ("lim")(xvec0){tan(pi/4+x)}^(1//x)

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

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

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  13. lim(x -> oo)(x(log(x)^3)/(1+x+x^2)) equals 0 (b) -1 (c) 1 (d) no...

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  14. ("lim")(xvec 0)((2^m+x)^(1/m)-(2^n+x)^(1/n))/xi se q u a lto 1/(m2^m)...

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  15. ("lim")(xvec1)(1-x)tan(pix)/2=

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  16. If f(x)={(sinx, x != npi " and " n in I2), (2, " x=npi):} and g(x)={(x...

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  17. ("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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  18. underset(xto pi//2)lim(sin(xcosx))/(cos(xsinx)) is equal to

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  19. If lim(xrarr0)(x^(-3)sin3x+a x^(-2)+b) exists and is equal to 0, then ...

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  20. If lim(x->0)(x^n-sinx^n)/(x-sin^n x) is non-zero finite, then n must b...

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