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

Use formula `lim_(x->0)(a^x-1)/x=log(a)` to find `lim_(x->0)(2^x-1)/((1+x)^(1/2)-1)`

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CENGAGE ENGLISH-LIMITS AND DERIVATIVES-All Questions
  1. Given ("lim")(xvec0)(f(x))/(x^2)=2, \where\ [dot] denotes the greatest...

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

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

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

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

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

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

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

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

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

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

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  15. ("lim")(xvec1)((1-x)(1-x^2)...(1-x^(2n)))/({(1-x)(1-x^2)...(1-x^n)}^2)...

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  16. The value of lim(x->0)([(100 x)/(sinx)]+[(99sinx)/x]) (where [.] repr...

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  17. The value of ("lim")(xto1/(sqrt(2))) ((x-"cos" (sin^(-1)x))/ (1-tan(si...

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  18. The value of lim(x->oo)((2^(x^n))^(1/e^x)-(3^(x^n))^(1/e^x))/(x^n) (w...

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  19. Let lim(x->0)([x]^2)/(x^2)=l and lim(x->0)([x^2])/(x^2)=m , whe...

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  20. ("lim")(xvec1)(xsin(x-[x]))/(x-1),w h e r e[dot] denotes the greatest ...

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